I believe Bill is correct. The running lights are grounded to the skin of the camper. Since you have some but not all we know the skin is effectively grounded and since the running lights are powered in a daisy-chain, I think if your remove the base and insure that the one screw holding it to the frame is clean and the place where it passes through the metal inside the light is clean as is the skin where it is attached to the camper. When you remove the lens, if the internals are rusted out, then a replacement is needed if you can't clean it up. That tells you water is getting in there and it is an excellent time to remove all of the bases and put in some new butyl tape to waterproof them for another few years.
However...the black wire from the socket brings power to the light bulb socket...if it is broken off then the only way to reconnect it is from the inside where the wiring harness for the lighting system runs....if you have no plans to gut the interior and replace that wiring system then you probably won't be able to reconnect the black wire to the harness. So, no luck with that one!