This is a continuing issue that I had starting last winter. The Jeep just kept dying. I ended up replacing the battery and the alternator last spring and things were fine all summer. This fall, it started doing it again, battery being dead and just not starting.
Part of the problem is, the Jeep is not my daily driver, so it it is not run on a regular basis. I have a yellow top (Carquest version) and it was fine all summer. I pulled all the leads off and trickle charged the battery a few weeks ago and it started up fine. Prior to that, if I started the Heep via a jump and let it run for a while (say 30 minutes), shut it off, and immediately tried to restart it, it wouldn't go. That's what makes me think it's the alternator. That, or the alternator just couldn't bring a completely drained battery back.
I don't have the idiot light, but I do have the volt meter, and it usually sits around 14+.
I need to go through and see if I'm drawing current anywhere, as it's on my list of things to do. I have a number of aftermarket electrical accessories, winch and lights, and don't know if I'm losing something there.
In the meantime, I was just trying to find out of it is the alternator or not, and was looking for ways to test it. I have a Haynes manual, but haven't checked it, so I will.