Really great guide @koltes, and good additions as well from @Prater, @Iroquois Confederacy and @Hodo. All players whose posts I can see great wisdom in, reinforcing my own experiences as a solo hunter.
For my part, I have always played in this solo style, and while I have nowhere near as many hours as Koltes and Prater do, my ~600hrs have been dedicated entirely to this kind of play. So, I'll offer my additions / observations / opinions for what they're worth.
The Neverending Puzzle
One of the most interesting things about the solo hunter playstyle is how much of a puzzle game it becomes. You need to find the right places to hunt, you need to anticipate your quarry and their movements, you need to anticipate the sheep dogs and their attempts to trap you, and you need to figure out your logistics to tie the whole thing together. Koltes has given some great suggestions about how to go about sorting this out, so no need to reiterate.
One thing, though: the player population is changing all the time, as are port owners, and the expansion and contraction of national territories tied to each can create and destroy hunting grounds depending on who owns them or has moved in near them. So, facts that were known a few days/weeks/months ago may still apply, or they may not. You really have to go there and do your scouting to find out.
On Hunting Grounds
Some areas of the map are much easier to hunt than others, due to the way the ports are aligned, the coastline is laid out, and the resources of the ports are configured. Some areas can be a deathtrap as there are many nearby ports that, if owned by the nation whose players you are hunting, can lead to the easy formation of sheepdog revenge squads that can close in on you from all sides. Other areas offer easier access to escape into the open sea where you will be much harder to intercept. Additionally, areas that are active in one time zone's primetime may be nearly dead in another. You need to find that "goldilocks" combination of a reasonable chance of success combined with a reasonable population of player traders to hunt in your prime gaming time.
Capping vs Sinking
I personally really like the challenge of capping player trade ships for later sale to the market, so I rarely sink a ship I've captured and am in fact pretty loathe to do so unless I'm fairly certain I'll need to make a hasty escape. I will often go through the cargo if possible, discard the least valuable / heaviest items to help make the prize ship a bit faster. And then one of my favorite parts of the whole process begins: the super stressful and exciting crawl back to your base of operations, hoping you escape notice and bring home your prize. It feels like nothing so much as being a leopard on the African savanna, trying to make off with your kill before the lions steal it away from you. I love it.
You won't get as many (or any) combat marks for doing this, but consider the math... if the capped TBrig sells for 40-60k at market, and combat marks can be bought for 1k each, you can potentially purchase 40-60 combat marks with the earnings from selling the ship, whereas sinking it will only net you 2 combat marks. Can you capture 20 TBrigs in the time it takes to sell one at market?
Also, as I'll mention below, I sail only unrated vessels while hunting, and I do not like overloading my hunting ship as it makes it very difficult to get away. I'd rather have the captured prize in fleet, and sink it, than hobble my fast hunter and turn it into easy meat for the sheepdogs. So I keep the prizes and sell them later.
Hunting Ships, Upgrades, Cannons, Repairs and Perks
Because I focus on capping traders and taking them as a prize, I find I need to really focus on bringing sail repairs, as I'll need to repair not only my own sails (either during battle or afterwards) but also those of the trader who I have captured. Failing to do this means I will be much more subject to revenge interception, as the trade ship will sail very slowly unless its sails are repaired. Curiously, despite "splurging" on fir/fir builds, almost all of the traders I capture do not carry sails repairs. When you're already sailing a vessel worth 50k or more in a capital market, the idea that spending 1/10 of that value on sail repairs seems like trivial insurance to try to hedge your chances of getting away, but most seem to "YOLO" it and do without altogether, so they can maximize the amount of cargo carried. I can't say I understand it, but I guess it improves their bottom line, and certainly my own, as it makes them much easier for me to catch.
Now, because I must bring enough sail repairs for both my ship and my quarry, I need to really optimize the rest of my loadout and ship upgrades. Like Prater and Hodo, I hunt exclusively in the Lynx and Privateer, with the latter being my favorite despite its poor downwind performance. I run Optimized Ballast and a Gazelle figurehead as a minimum, as well as 4lb long cannons, which I prefer to 6lb mediums as they are just a bit lighter and nearly as effective. And they reload much faster than 6lb longs, which I feel is important. You want your reload time to be less than your stern camping 180* turn time, so you can fire as soon as you've made your turn and can keep your speed lower and your s-turns tighter, making it much harder for the quarry to hit you with broadsides. I also carry some Hull Repairs and Rum, with the goal being to keep my Privateer or Lynx at 15kts max speed while still having enough repairs to do my work successfully.
My preferred perks: Fleet 1, Area Control, Prepared and Rigging Specialist are mandatory for my playstyle. I am undecided about Double Charge vs Double Shot, though I think the former would be better for my small ships (every bit of extra penetration would help those 4lb longs). Fleet 2 is also tempting for those times when you hate having to choose one of the two ships you've captured. I'd rather sink neither, to be honest.
Escorts in Fleet: Deterrent or Opportunity?
One thing I didn't see mentioned above was that many traders will bring along a warship in fleet to provide some measure of defense. Sometimes, however, they make a mistake and bring a good upwind warship (i.e. Lynx, Privateer, etc.) along with a good downwind tradeship (i.e. TBrig). When I see this, and that the player trader is on the trade ship and leaving the AI to command the warship, then I see it as a free warship for me to capture. In almost all cases, the player will command the NPC warship in his fleet to attack me, and I will happily sail upwind - dragging the NPC warship after me - and then chain its sails and board it while the player in the trade ship escapes. Granted, the warship might not be worth as much as the player trade vessel, but on the other hand, I've just acquired a "disposable" backup hunting ship that I can use to do some extra silly / risky things that I'd rather not commit my main hunting vessel to. In either case, the "threat" the fleet warship is meant to represent is not interpreted by me as anything to be afraid of, but rather as another opportunity for gain.
It Is Better To See Than To Be Seen
Whenever I am in the open world, I am constantly swiveling my camera 360 degrees and clicking on every sail I see. I used to assume that this is what everyone does, but with time I've realized that many, especially when they are in their "safe" home waters, get a bit lazy about this. They are not AFK per se, they are simply "cruising", like how sometimes happens when you're on a long drive on the highway and you realize you've been driving for a few minutes without any consciousness of doing so. Maybe they are tabbed out, maybe they are chatting, who knows, who cares.
This has many implications: I can sometimes simply sail up to someone, get in position, and tag them and they only react once they see the circle go around their ship. Other times, it means I can tuck my ship into a part of the coastline where I am more-or-less in plain sight, yet I will watch as ship after ship sails right past me, without taking any notice whatsoever... because, in their mind, there's "nothing interesting" about that stretch of coast they've sailed past countless times, and they somehow fail to even think that something might be hiding there, waiting to pounce, so they don't bother even looking (they're probably scanning the other way, to the open sea, or who knows what). It's kind of amazing and adrenaline-pumping when it happens, and it happens a lot!
Likewise, because I am constantly scanning, it is extremely rare that I am myself caught by surprise, and I often see other people well before they've seen me. One thing I learned while hunting around Jamaica with @Jarlath Morrow is that you really want to avoid being seen if at all possible. Smart players will quickly announce your position via their National chat and then all the traders will bunker down till you've been caught or left the area, and the sheepdogs will come out in full force hoping to kill you (as they should). Which means that I'll often tack or gybe away from a player character I spot, extending off in the other direction in hopes that they'll have missed me and fail to report my position. Quite often, it seems I am successful, as I later find traders sailing nearby, seemingly without any awareness that a pirate is operating in the area (of course, reports to national chat are only helpful if you actually read them).
The Myth of the Defenseless Trader
There is a great deal of arrogance and disdain expressed against those who hunt player trade ships, as these hunters are believed to be attacking "defenseless easy prey" and the ensuing fight to capture the trader prize is "not PVP." Based on my experience, when I hear someone make these claims, I am pretty confident they have never tried done much if any hunting, certainly not in a 7th rate, nor as a solo player, with only the ship and upgrades they have created/earned/grinded themselves (i.e. without the benefit of their clan's community resources). Really, if you've never hunted alone, in enemy waters, with no clanmates to back you up, you are in no position to say anything about what this kind of hunting is like, because you simply don't know. Those who hunt know better, and do not say such things.
So let me come out and say it: even prior to the patch that allowed traders to be fully armed, they were far from defenseless. I have had traders try to ram and capsize me, I have had them try to break my bowsprit off, I have had them engage in all kinds of wild behaviors as they throw caution to the wind and do anything and everything they can to stop me, by any means necessary. And this was before they had cannons! Very few are passive and most will never surrender no matter how hopeless the odds, happy to see their ship sink or explode or otherwise, if it means depriving me of a prize.
The Lynx continues to be very easy to capsize and the danger is greatest when you attempt to turn the trade ship into the wind. If you mistime your push, you can easily get caught under the bow of the trader and in only a matter of 2-3 seconds be on your side in an unrecoverable broach. Is is especially dangerous if you have not sufficiently chained down the trader's sails, but even then the danger persists. The Privateer is a bit better but not immune, though its greater mass means the margin for error is a bit higher.
Obviously, a Surprise is a different kettle of fish altogether, and these issues facing the unrated ships are not considerations. However, Koltes has done a good job of describing the many challenges facing the Surprise captain - as the ships themselves are so competent, they are guaranteed to draw revenge fleets, so they come with their own set of issues. And while I have yet to capture a player trader in an LGV or Indiaman (as I very rarely see them), I am sure it presents a genuine challenge to the Surprise captain and isn't simply "easy meat."
In any event, now that traders can be fully armed, they can be quite dangerous to unrated hunting ships fitted for speed, at least if their captains are competent at sailing and shooting. The only time I've been sunk by another player since wipe (roughly 200hrs of gameplay in which I've captured dozens of player trader prizes) was when I persisted too long in attempting to capture a TBrig sailed by a very competent British player who was an excellent shot, too. I could and should have broken off my attack, but I kept going for "just one more pass" rather than taking a cold and rational look at my ship's condition and realizing the capture was hopeless. Suffice to say, if you come across a competent captain, that trade ship can be a very worthy opponent. I've had better fights from armed traders than I have from warships, by far. Much more tactical, much more challenging, much closer of a match. They are defenseless only to the extent they choose to be.
Which brings up another interesting observation: like with sail repairs, many traders chose to go unarmed, or with only stern cannons. Why this is the case, I have no idea. I've also seen instances where a trader has cannons, but forgets to use them. Far be it from me to tell him otherwise, but it still sort of boggles the mind. I suppose it's a sort of min-maxing theory: no repairs, no cannons, full cargo, damn the horses and go for it. Works for me.
Stick To Your Plan (Or You'll Plan To Fail)
It takes time and practice, as Koltes notes, to come up with a system for capturing ships successfully. While learning to tag, or prevent ships from escaping, or to chain sails, or to grape, or whatever, you will fail many times. Sometimes you will sink. Many times you will be mocked in battle chat as your quarry slips away and you find yourself, due to the mistakes in your approach and execution, incapable of doing anything about it. Prepare to be humiliated, as this is part of the learning process.
Later, once you've got things sort of figured out, and you feel like you know more-or-less what you're doing, you may start thinking you can improvise, or "do things a little different this time." Actually, you probably can't. The system you developed through all those failures is probably a good one, and better than what you try to make up on the spot, and it's one you should stick to in most cases. Failing to do so is courting disaster (see my anecdote about getting my hunting ship sunk above). Most importantly, know when to call off an attack - be it at the tagging phase, or during battle, or when you have to sink a ship to get away (be it in battle instance or later in the OW). Your hunting ship is the most important and hardest to replace tool in your arsenal, and you must try to protect it at all costs. You will always be able to find new prey, probably just a few minutes later, but it might take hours to replace a heavily customized hunter, especially if playing solo. Try to stay cool and calm and make this choice - to break off the attack or not - a business decision first and foremost.
I've gone and written a small book, and apologies for that. But this thread was long overdue, and I'm very pleased at the high quality of content presented. Kudos to @koltes for the initiative. I hope my own contribution is helpful for those considering the truly solo hunting approach. The rewards are well worth it; it is a unique and singular experience within Naval Action, one that few allow themselves to experience. So much the better for those of us who do... but, the world is out there, and it's yours for the taking, if you're captain enough to do it.