Confirm the wire from your tow vehicle for the drivers side is sending current to the rear.
If at the wires at the rear you're getting power, but no light:
1. Check to make sure bulb is good
2. Check to make sure (with power off) the terminals are clean on the socket
3. Make sure the trailer has a good ground to the frame AND the body. Water and/or rodents may have caused issues with the ground to the vehicle/trailer which can do really screwed up stuff with lights (some working sometimes, only one side, causing them to be dim, both blink, weird stuff).
4. make sure the contact point from the light socket side to the trailer is connected with a clean connection (again ground).
If none of those solve the problem (but you have what you need electrically in back), then you may need to run wires inside the rear compartment from wherever the shop ran back, over to the license light and drivers side and splice back in.
Also, under the front center window, there should be alittle cover about a foot off the floor, check with a test light that each terminal does what its supposed to (i.e. with left turn signal on, one terminal should cause the light to flash on one of the terminals).
Good luck, hang in there, you'll find it!
Scott & Megan
Help us restore Wally Byam's 1955 26' European Caravan Trailer!
Needed parts list and blog: https://wallybyam1956.blogspot.com