Hi
Many thanks
To be honest, rather then taking parts apart I would run a cable to the reverse light - so it powers on BUT make sure the headunit is expecting a 12v feed first or you could damage your headunit
Have you checked your camera rca lead to see if there is a red wire already existent
If so, and your headunit expects 12v power on the lead to switch screens, all you need to do is extend the red wire to your reverse light wire in the rear light cluster (it is very tight though with no room)
I run my cable underneath the door bottom trim inside
I am sorry though, I am not an electrician so cannot help with where you would find reverse light power closer to headunit
As I said though, make sure you know your wires and power feeds of wires, or you might damage headunit
Many thanks and good luck
John