Is this an electrical problem or something else?

'96 XJ, 222,xxx miles, 4.0/AW4.

Lately I've been having some idling/running issues with my Jeep. It seems to be on and off, sometimes it runs fine, others it doesn't. The major issue is it's not idling very well, it likes to die at stop lights so I have to do a bit of a brake stand to keep it running. When I give it gas and go it drives just great. Even does a smokey burnout just fine. I took off the TB and all the sensors and cleaned them, but it didn't seem to help.

Then, last night it wouldn't start. Classic sound of a dead battery, a few turns and then nothing. It was already on a charger that said it was fully charged. So I jumped it, and it started fine. Bad battery right?

No. Now it starts fine again, just like normal. Occassionally it turns over real slow like the battery is low, but I don't think it is. I have an Odyssey sealed AGM battery with 2/0 battery cables and a 165 amp alternator. I have cleaned all the connections, so I should have plenty of power.

So what I'm wondering, is it possible the idling problem has something to do with this other mystery electrical issue? Or are they two seperate problems? Would a bad battery or alternator make a 4.0 idle bad, but run great?

A bad battery or poor connection would indeed mess up the idle and other issues, especially if the battery is cutting out of the circuit and causing the engine to run on unfiltered alternator output. Chrysler electronics are fairly notorious for battery sensitivity, and it's often difficult to keep one running after a jump start if the battery is not taking a charge right away.

First I would make very sure that the connections are good, clean them again (don't forget to ream/brush the posts and connections to get rid of oxidized layer) and make sure that all grounds are correct. Make sure the starter end of the cables is good, check the ground strap from firewall to engine, and the ground from battery to engine as well. If you have bolt-on battery terminals, make sure the terminal to cable interface is not oxidized too. If possible check voltage when running and see if there's variation or cutting out. I've had battery issues in the past that resemble your symptoms, so if nothing else seems to work, it might be time to try a new battery. I never figured out why mine seemed to work perfectly one day and be dead the next - perhaps a short or an internal problem - but it did, and a new battery solved it.