The last one I did with the same symptoms was a 2005 Suburban. Traced the problem to the under hood fuse/relay box. Had to replace it, was shorting the same way with the high beams. The jeep is called a totally integrated power module. Please have it diagnosed first, your module will have to be programmed before it will work, doesn't mean this will fix your Jeep.
Don't think so; Thought that on the other one, checked switch, sensor, wiring to the BCM and out of the BCM to fuse box. While testing wiring realizes something else was activating and was shorted to head light circuit. WA LA headlights came on as well. Hope it helps.