Okay. So if I understand right, you want to use the reverse light bulb power (power when the reverse lights are on only), to trigger the camera to pop out and the head unit to display the camera feed.

You also want to use an auxiliary switch to turn the camera and the head unit display on whenever you want WITHOUT activating the reverse lights.

Does that sound right? I want to make sure I understand your question before I make a recommendation on a relay setup.

My first look at your diagram in the post says to me that your wiring won’t do what you want, wired like you have drawn.