[BB_TX]

I am with the guys above. Use the voltmeter to determine whether you have voltage at the socket or not. (Touch the meter ground wire to trailer frame rather than the ground connection on the socket.) That tells which direction to look next.

If voltage at the socket, but lights do not work, then it is most likely a ground connection problem of the light fixture ground wire. Although that ground wire should be common for the taillight for that fixture also. Does the taillight work?

If no voltage at the socket, even when using frame as ground reference, then there is a connection problem between the socket and the 7 pin connector, possibly in the junction box under the pin box. Possibly in the wire connection where the fixture wire connects to the wire from the 7 pin harness.