Okay, that makes more sense. If you got 12V, and you measured with one multimeter probe on the chassis, then you did NOT test the connection from the vehicle ground all the way to your bulb housing's negative contact. I think I mentioned this earlier, and someone else described how to test this segment.

If you measured using one probe on the chassis, then it is IMPOSSIBLE to get 12 volts on each pin (unless you shorted them while measuring!?).

Okay, this makes more sense. So to make sure I understand:
1) probe to housing pin and probe to chassis ground = 12V
2) probe to housing pin and probe to other housing pin = no voltage
3) swapping out the housing with a known-good housing+bulb combo = no light

If the above 3 are true, then the problem is almost certainly in the ground connection between the vehicle ground and the outside connector to the housing.

Your next steps are to connect the multimeter to the outer connector of the housing, one probe to each pin, and confirm there is no voltage. If this is the case, reconfirm that you can still get 12V with one probe on the positive pin and one probe on vehicle ground. If this is the case, then you've ruled out the housing and nailed it down to the ground wiring/connector. If you're lucky, it's just a bad joint between the connector and the ground wire of your housing harness. Inspect it carefully.

If there's nothing else obvious, rather than tracing the entire wire back and testing for continuity a couple feet at a time, I would just take it to the dealer. A lot of times, they'll just warrant the repair. And if they don't, I would insist that they prove that you were responsible for whatever damage they find. Did you do something you're not telling us?