Find where the ground wire is attached to the frame of the RV and then see if it's loose or looks corroded. If either of those remove the connector and clean the area well and reinstall it. There may be more than one ground on the frame.
Salem 29RKSS Pushing a 2500 Mega-Cab CTD!
Gotta go campin!
Clean the contact area of any and all grounds that are related to your hitch and camper. The area should be free of rust, debris and paint. Reinstall with a new screw or bolt if needed and make sure it is tight. If you still have issues after that you may have a bad connection between the TV and Trailer. Easy way to test the trailer wiring is get a test light probe. About $10 or so and it make life a lot easier to see if you have power from your TV. At the connection point. Inspect all wiring. Possible light bulb being burnt out, or installed incorrect. 1157 bulbs are the 2 fillement bulbs and if one wire breaks or it's put in backwards it will have the same effect as a bad ground. Hope this helps, good luck with the repair.