I don't know what the typical life of the camera is, but having it on all the time will certainly make it shorter.
Use a diode so that you can have two inputs (reverse signal or brake lights, power from head unit whenever you want your rear camera on) to keep the input signals separated from each other. Otherwise, when you're driving along and you decide to view your camera to see what's behind you, you'll activate your reverse lights as your moving forward. Will confuse other drivers on the road.
Diode: Amazon.com
Attached is a wiring diagram I made up when I wired my backup camera. My particular head unit didn't have the option to turn on rear camera on demand, but did have a front camera on demand option. I used a splitter so that my rear camera fed both the front and rear camera ports on my head unit.
View attachment 412836
I gotta study up on this lol. I havent wired anything since my car's remote start and that was 8 years ago.