Just order a simple game camera and set it in the back window of your car.
https://www.amazon.com/Optics-Game-C...8&node=3413551
A typical rearview mounted camera may not capture something at the rear corner, plus the cost of getting something installed, having your interior torn down, etc to solve a very specific temporary problem wouldn't make sense to me. If you want one for other reasons then go for the full install. With the game camera you can buy it this afternoon and have it ready to go immediately.