One of the lighting circuits is back feeding the camera circuit. Plug corrosion, wires pinched together, dual filament bulbs, etc. I either missed or didn't see which particular lighting circuit was back feeding the camera. Isolate which lighting circuit is turning the camera on - parking lights, fog lights, reverse lights, etc. Be advised turning on the headlights will also turn on parking lights, same with fog lights.
If I had to guess a close inspection of the parking light circuit at the rear where it is running near the camera or reverse light circuit will locate the problem.
Look particularly close where the trailer wiring harness was installed. Something may have rubbed or corroded.