I just had this happen multiple times on a recent trip up to CO and experienced the same; battery light would go away after turning the Jeep off, yet return within 40-50mi. I was concerned it was the alternator as I'm on my 2nd one (I'm awaiting an APEX now). I made it to CO and took it into Specialized Truck and SUV in Frisco (great shop & team) who performed a full charging system diagnostic, pulled codes, etc. In my case, they were able to see a voltage spike of +15V in the history meaning the system thought to push more out of the alternator to compensate for a lack of charge. They replaced my Optima with an Interstate and saved my wheeling stress... made it back home without issue and I haven't had the issue again. All voltages on & off are stable. Saying that, I am ordering an IBS to keep in my kit just in case. Get somewhere to pull the codes (preferably not a dealer), but I'd start with the battery particularly if you're seeing +14V consistently while driving.
Put your vehicle in "Run" (engine off), let everything boot up, and check the voltage on the dash.... voltage should be somewhere ~12.2V - 12.6V on a good battery. ~12.6V - 12.8V fully charged and rested.
Electrical voodoo sucks..... fuses, battery, alternator, IBS, wiring/grounding, etc.... I can fix most things in the field, but I'm not an electrical expert by any means.
