Had a somewhat similar situation on my 64 flatbed. Since the main rails of the bed were separated from the frame by wood, there wasn't a good ground, even through the u-bolts. When I installed the junction box to connect all the bed lights with the cables coming from the cab and turned on the running lights, the backalarm sounded and all the lights came on. Ran a ground wire from the bed to the frame, problem cured. The backalarm and other lights were the paths of least resistance for the current.
