We had similar issues with ours. We got a 2008 Ford F250 with tow package. We had the trailer towed home by my father with a 2004 F250. All the way home, the reverse lights were on the camper (didn't notice until home). When we plugged in our 2008, same thing occured. We were lucky we didn't blow something up.
I had the dealer we bought our F250 from check the wiring on the 7 plug in our TV while I watched and made sure the diagram on the cover of the connection was correct. Then came home, unscrewed the cover on the end of the camper umbilical and located the white wire. This should be your ground. Using jumpers from a battery, I connected the grounds together. Then using the positive jumper, clicked to each of the other pins to see what each went to. I found that the reverse pin on the trailer was going to the positive feed (charge) of the TV battery and vice versa. Finding the brake pin (we have aftermarket electric disc brakes on the camper) was a little tricky. When I touched the pin, had the wife listen for a click at the wheels. It worked well and we only had to swap 2 wires on the camper umbilical.
I figured it was better to change the trailer wiring than both tow vehicles since it seemed the TV's were standard (at least for both vehicles we would have towing it).
Tadd, Beth, Grundgetta and Weeble
Proud to be Air #37137