I don't know what kind of TV you have but my 2005 Dodge Ram and 1999 Chevey Z71 both have fuses under the hood that are dedicated for the left and right trailer stop lights, these fuses don't effect the TV stop lights. i had that happen before and foung the fuse for the left trailer stop light was blown.
Manny, wife Tammy and our son Sammy and our dogs,
Cowboy and Starla.
1999 Z71 Extended Cab, 5.3L, 4:10, with 4" Lift.
2005 Jayco Jayflight 28BH.