Best bet would be to call the service department and ask them what they would charge to diagnose the problem.
Sounds like it might be a poor connection or maybe oxidation on a pin. You can check the two connections in the tailgate, one near the camera and the other where the tailgate opens on the bottom center. If that is the problem you can get electrical anti oxidant cleaner and spray on the pins.
If it is the camera, one member just had his short out, a replacement will most likely run from $150 to $200 (estimate)