For the power, you might want to try the fuse. If you trace the battery wire there is usually an inline fuse on the cable. Some campers have it under the trailer on the main battery cable.
The only thing I can think of with the brakes is either the emergency brake actuator on the trailer tongue, or possibly a corroded 7-way connector. On my last Chevy, the 7-way connector on the truck would get corroded and make the prodigy think a trailer was connected when it wasn't. But, that only happened in the winter and was probably from salty road slush which conducts electricity very well.
Ray
