Does the camper plug into the trailer harness?
If you end up doing that, I leaned the hard way that the 3rd brake light needs to be connected to both brake wires by way of a special trailer 3rd light adapter. They call it a logic unit, but I suspect there is no logic to it. It keeps the 3rd brake from flashing with the turn signal.
If you have to wire from scratch, you could also tap the existing 3rd light from the truck and run a wire there.