Start by proofing the "Female" connector at
the TV. (Use a test light)
Next - double check the "male" plug that connects
to the TV. They do corrode, get old and worn.
If you know for sure you are getting good stuff
all they way back and into the wiring of the trailer, then
begin changing bulbs, cleaning connectors and grounds.
You must know that you are good all the way back and into
the trailer before working on the trailer.
As "FrashAir" mentioned above, clean and tighten every
ground connection....the skin must be a good conductor
and the frame....make for yourself new skin and frame ground
connections - make em big, clean and strong - remove all doubt.