I don't have a solution, but I have experienced something somewhat similar with my 2007 Grand Cherokee toad. A few times I have noticed the headlights come on after I brake heavily. They go off a bit later, so I had no battery drain, but still a very strange thing, and clearly something is not right.
Not sure if the diodes on the toad stop lights have somehow gone bad or what. Not sure what else could cause it. If this happened during the day, not sure I would notice in the rearview camera, but it definitely gets your attention when driving at night.