So this black wire is under the dash?

 

No, it is near the driverside headlight.

 

The black wire is a ground at the headlights.

With your meter, from the black wire to ground there should be 0 volts, not 12. From both the light green with brown AND the violet with white wire you should have 12 volts to a clean ground.

That's it. The socket can be bad. Use a paperclip or something if you have to to measure from the socket.

There are no other splices in the wiring from the CTM, it goes right to the headlight socket.

You might be looking at a bad CTM.