Welcome to the forum
It’s easy to isolate the problem. Make a short jumper wire and do the following.
Look at your second picture, 12V positive is the 11 o:clock position.
Jumper from 11:00 to the 1:00 and the running lights should work.
Jumper from 11:00 to the 9:00 and the Right turn/brake light should work
Jumper from 11:00 to The 3:00 and the left turn/brake light should work.
If they do the issue is most likely truck/7way socket
If they don’t the issue is in the trailer wiring.
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2012 Copper Canyon 273FWRET being towed by a 1994 Ford F350 CC,LB,Dually diesel.
Airlift 5000 bags, Prodigy brake control, 5 gauges on the pillar.Used to tow a '97 Jayco 323RKS.
Now an RVIA registered tech. Retired from Law enforcement in 2008 after 25+ yrs.