That's a good question actually, and I am taking a few shots in the dark
First of all, I think that Indians in later times would sometimes use watches. It would not be an item that most people had but let's assume in most groups there could normally be scientifically inclined guys who owned rare white mans items like the one to measure how old the day was. Timekeeping is very useful in certain situations, like predicting when someone arrives or how long it takes, and it is certainly scientifically fascinating when you are so inclined.
Or maybe it wasn't even necessary. Most Indians would have been able to take time from the sun. I'm pretty sure that their skill in this area would surprise us today. There is a tribe in the Pacific that can exactly locate their position on the ocean by looking at the stars, and could theoretically locate any position within the the entire pacific.
In the end all stone age people who were advanced enough developed such skills just out of necessity.
I think almost everyone would be able to look at the sky and make a very good estimation of the following:
- cardinal directions (or some similar concept of direction)
- weather forecast for next 24h
- time of day (approximate to 1h or less)
There are also many other usueful hints, for example certain bird songs can pretty accurately tell of weather, time and many impending dangers.
And people have an inner clock too, this should not be underestimated either!