This is a tough one. The 12 volt
line that you talk about splits (somewhere) with one leg going to the rear two vent lights and the other half going to the control panel (water pump) and then to the front vent light and fan. The wire continues to the 7 pin connector to your TV. That would explain why the circuit works when connected to the TV. If the rear lights are working without the TV connected, the break must be where the split is. I would guess that that connector would be running along the roof somewhere.