[dana44]

Sounds like there is a short on a light circuit. Most likely there is a wire that is grounding to the body somewhere from the sounds of it. Unless someone else has an answer, I would suggest pulling one fuse at a time to see if the battery light goes out to help isolate the circuit being grounded. It most likely will eliminate which circuits are good if the light stays on. Also just do a quick check of the wiring harness to ensure you don't see any damage that is obvious to speed up the process.

 

[ImperialCrown]

Welcome to Allpar. There was a PCM software flash for false battery light illumination. See Chrysler TSB # 18-007-07. PCM software flashes should carry an 8/80 warranty.
There will be a fault code stored in the PCM as to why the battery light is on.
If you have the new software already, it doesn't have to be a charging problem. It can be as simple as a battery temperature sensor in the battery tray being unplugged or defective.