truck reverse lights always on when truck camper plugged in

Assuming your truck is wired right, It sounds like there are some crossed wires. You can look at wiring diagrams, but 7 pin connectors usually make it easy to swap wires with wires secured by screws. With some trial an error, you can straighten the wires out even if your truck has a few things reversed. There are plenty of diagrams available for 7 pin connectors, or if you buy a new one, many come with wiring diagrams.