I'm 100% sure this is the locker sensor, as I've spend the entire weekend with the carrier assembly out of the differential. When I put my 05 Rubicon on 4L and hit the locker switch, it just flashes.....untill I pull out the little switch which protrudes inside the differential, then the light on the dash comes on continuously. My wire is exactly, 100% looking like yours.
I unscrewed the sensor which goes into the differential housing (you should be able to find yours pretty easily as it's where that broken wire connects), however now when I screw it back into the differential, the inside switch is pushing the locker plate and partially engaging the locker. I unscrewed the front locker indicator switch to examine that and now when I screw it back in, the front differential is partially engaged.
Some people have told me that the entire carrier assembly needs to be removed to install this switch properly. Have you come across any new information since this post?