In the past, like 40 years ago, when I ran into something like this I would run a large battery of tests to determine the problem or if there was one and if so where it was.

But today it is easier to just run down to Autozone and have them test it for free. I'm not trying to shill for AZ, there are other suppliers that will do this service quickly, for free, with the alternator still on the car.

The problem may be simple or it may be complex, but to start with you must know: Is the alternator working as it should?

They can tell you, and then you can move on from there.