Do not depend on the ball or safety chains for the ground/common side of the circuit.
You can test the lights on the coach using a battery charger. Connect the black lead of the charger to the frame of the coach in a clean shiny spot. Then test each of the remaining terminals on the plug in the side of the coach. Using the red lead of the charger.
Once you know the coach lights work. You can sort out how to match it up to the TV.
Knowledge: "A gift to be shared. A treasure to receive."