Backup camera install on 67 mustang

Sure. Find the wire running to the reverse lights, run a tap (the correct way) and use a small automotive relay to activate your device.

I do not think however, that what you actually want is for the screen to only get power when the reverse lights come on. Nearly all electronic devices have an initialization period after power-up. Applying power to the screen only when reverse is activated will probably induce a delay.

Most of these kinds of devices have a power (on when the car is on) and an 'activate' or sense wire. I'm not looking directly at your kit but I would hazard to guess that your kit is similar?