I'm assuming you're connected to the tow vehicle? I know on certain GM vehicles you have to add a fuse to get 12 volt power through the factory trailer hookup back to the camper, this may be why your not getting power. I would check the truck plug to see if you have power, then check that the factory camera wiring is actually connected and check the fuse box for a blown fuse. It seems silly to have a backup camera that requires the running lights to be on.
Of course this is assuming the camera runs off of 12v system and not the 120v
2014 Aerolite 213 RBSL
2016 Chevrolet Colorado