backup light ground
 

Hello all,
I just picked up a 61 olds 88 and the backup lights aren't working. Diagnosed it to lack of ground in the housing. The issue is I'm not sure the best place to try to get a good ground. There's paint on the outer housing so it won't make contact there - remove paint?. The bolts that hold the housing look like they might work but have a few points of contact that could fail. I'm wondering if there's supposed to be a ground wire coming in with the hot wire instead. If so I'd have to tear into the socket container and run a new wire. There's only the hot wire now.

how does this work stock?

thanks!