If only the exterior lights are connected, how can the camper draw anything from the truck when the truck is off? When no lights are on in the truck; no lights can come on in the camper, right?. All lighting pins in the plug are at 0V, or the respective light would be on on the truck as well. Provided everything is wired correctly on the truck side. The wiring for the exterior lights bypasses the camper battery and the rest of the camper electrics. In that regard, the camper behaves like a trailer without any power of its own. Or are there campers out there that do it differently?
So there must be *some* connection between the +12V charge line and the camper elecrical system, somewhere. I think. Can you disconnect the +12V at the truck side of things? Be careful though, dependig on how the truck side was wired, the line is fused to 30 or so amp - or maybe not at all if the plug was installed by someone who didn't know what they were doing.