You can test ground the socket with a wire and eliminate that possibility, and if you use the socket for the ground of your light and it works it's not a ground problem.
If you have the bulb with the correct contacts then it pretty much has to be the spring in the socket not pushing the contact pad up enough for the bulb to make contact.
(You said everything works separate)
One thing I managed to figure out is that the blinker side of socket doesn't work unless the headlight switch is on in either park light mode or all the way on in headlight mode. If headlight switch is off, then the blinker side doesn't do anything.
