Damn, not that hard.
Your backup cam will have 3 or 4 wires. A +12v, gnd, and signal (1 RCA or 2 wires - 1 pos, 1 neg).
You connect the +12v to switched 12v, ground the ground and hook up your signal wire to the head unit or TV controller.
The head unit or TV controller will take care of switching between the reverse cam and other sources. Your head unit or TV controller needs to be connected to the reverse lights, usually on the positive lead. Which your controller already is from that I'm reading.
2013 F30 328i - Melbourne Red
2011 E90 M3 - Monte Carlo Blue
2004 E46 M3 - Imola red