If you get 12V at the socket, everything is good except....the socket, or bulb. Make sure the "new" bulb is actually good, they have been known to be bad from stock....and make sure it is 12V and not 24V. They look the same.
Make sure the contact for the bulb is actually "contacting" the bulb. Only 3 faults on a DC circuit...open, short, high resistance.