Ok...here is one option.
Auto:
Power EVERYTHING off of 12 volts from the battery, or 12 volts from where ever. Don't use the activation signal (the reverse lights coming on) as your power source too. Simply use the reverse lights as your activating signal. Hook up your camera and the reverse lights that come with the camera to transistors that connect to your main power source, and connect a wire from the reverse lights (your signal) to the base of the transistor. When the reverse lights on the truck come on, they will sat. the transistor, and activate the camera. The same goes for the lights that came with the camera.
Manual:
Simply run a line that shorts the transistor out of the line with a switch, once you flip the switch, you short out the transistor (not literally short, more appropriately
BYPASS), and activate either one, or both, the camera and the camera lights manually.
I can provide a schematic if that will help.
I hope this makes sense.
edit: A relay will work also, of you would like to avoid using transistors.