Problem with Tailights

Both brake, tail, and back-up lights work until I step on the brake or put the car in reverse. When I do the right rear (passenger) side light apparatus shuts off completely

bulbs and fuses are good. An aftermarket trailer light hook-up was installed but I have never used it and have never had a problem. On visual inspection it doesn't appear to have a ground. All connections within light cage have good continuity.