Is there a receptacle on the left front corner of the truck camper about 1 foot up from the bottom?
Normally, the TC exterior lights for driving (tailight, brake and running lights) are connected directly to the truck lighting system, either to the truck trailer hitch connector or to a special connector installed in the front left wall of the truck bed. In this case, you need a wire harness or "pigtail" to make the complete connection.
This connector may also provide 12 volt power from the truck alternator and battery. This circuit would be connected to the converter and battery in the truck camper. The battery or converter in the TC will not power the exterior driving lights on the TC
Rick
04 GMC 1500 4X4X4, 04 Sunlite SB