I had the same problem once and it took me a long time to figure it all out, so I will see if I can give you some clues. If your TT is old enough, many of the old ones used the siding to provide a neutral that carried the return from all the outside lights. Often the fixtures would work their way loose from the siding and then the lights inside the fixture would not work, or work oddly.
You may have a brown wire, a green wire, and a yellow wire. Those are the positive feed to the rear lights. Connect your negative from a good battery to the ground on the TT, someplace on the siding or frame, and touch the positive to those wires to see what happens with the bulbs at the back.
If nothing happens, then you should either find a way to see the back of the rear lights from inside the TT, or if necessary, remove them off the back of the TT and connect negative to the metal frame of the fixture, and positive to the filament leads to see if the bulbs work.
Only once you get the actual fixtures working properly can you then try connecting your wires to an actual plug.
PM me with your results from this and I will keep working with you. I have fixed many rigs and know how to fix brake/run lights that operate strangely with amazing results.
