The snap in type socket you have there is easy enough to access in the trunk. These reverse lamp fixtures are impossible to access from behind (cross member in the way). So yes you'll pull the fixture to replace a bulb. If you have loosened the socket to spinning at the crimp to the housing, you may have broken its chassis ground path. It may work intermittently. If so, you'll need to add a ground wire similar to what that other socket has. Same condition is found at front park/turn fixtures of 67 fish and other cast metal fixtures with fixed/crimped sockets. Good luck with it.