As mentioned there are previous threads on tail light issues that center around bad crimps on the wires that go to the socket that holds the bulb. A voltage check at the socket with the bulb removed compared to a voltage check to the wires just before they go into the socket will tell you if this is the case.

To test the wires before they go into the socket, use a sharp pointed probe or a pin attached to your meter lead to pierce the insulation. For this and the socket voltage check you have to be very careful not to short or ground out anything during the test or you could damage other circuits or one of the control computers in the vehicle. That will be expensive! If you want an example of this - look up the threads where people changed to LED lighting without disconnecting the battery.

I would find a good ground and attach the negative meter lead to that so you have your hands free to then test for 12 volts in the above two places. Have a helper step on the brakes when you are ready. Seriously - if you are unsure or not used to electrical troubleshooting, or using a volt / ohm meter then refer this issue to someone who is. You can seal the hole you made in the wire, during the before the socket test, with some of that liquid rubber stuff or nail polish. Also look for bad or loose connections, broken connectors, corroded pins or sockets.