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I own one, they are great. It's nice to be able to apply ground and 12v when you're poking around.
You said light socket, but you need to ground the bulb base and try it. The sockets can loose their ground to the housing. Tail lights working doesn't necessarily tell you for sure that the brake light is getting the ground it needs. Some the sockets are so sketchy about grounds that I even solder a ground right to the bulb base itself.
I eliminated the socket altogether and made connections directly to bulb shell and filament contacts. Still nothing. I even tried it with jumpers straight off the kick panel connector
First... Confirm your fixtures hole diameter ( I'm thinking it is 3/4" ). Google 1157 two wire socket. You should find replacement sockets and/or renew parts for the socket you have.