Adding an aftermarket backup camera

Despite the Prius having the best rearward visibility ever, my wife is used to having a backup camera, so I am adding one to my car.

The kit says to wire the power to the reverse light. Since this camera is intended to be mounted on the license plate, that will be difficult.

Is it safe to wire a camera and its transmitter to the license plate lights?

This should be off when the car is off, so it won't drain the battery, but it will require turning the headlights on to use the camera. Also the camera will be on when the headlights are on. This might be okay.

What I'm wondering is if there is any electrical reason I shouldn't do it this way, or is there some easy way to get a wire from the hatch to the reverse lights that I am missing?

Or better yet, is there something on that hatch that only comes on when the reverse lights are on?