The typical camera/monitor system has two possible 12 volt feeds. One is the power switch, normally located on the monitor. The other power feed comes from the backup light circuit. My guess is that you are getting 12 volts bleeding from the brake light circuit into one of these two power sources to the camera and monitor.
The difficult part will be finding the source. It could be wiring rubbing enough to wear through the insulation, some type of short circuit in the backup light, a wet spider web in the wrong place, or numerous other possibilities.
Maybe some other forum members will have ideas on how to troubleshoot this problem.
Fred & Vicki
Richmond Hill, Ga
2000 H.R.Endeavor/Freightliner/330 Cat