If you have all of the voltages from the truck's plug, you know that's good. Go to the trailer. make sure you have a good ground from the neg post on the battery to the trailer frame. Then connect a wire to the pos side of the battery and touch each of the pins on the trailer plug and verify that each of the lights work. if they do, then you have eliminated a broken wire, bad grounds, etc., and you won't waste a lot of time with what-ifs and second guessing. if you can make all of the lights work using the 12V from the TT battery, all that is left is a mismatch between the plugs. Trailer manufacturers like to use cheap components, and they usually use Bargman which are known to have issues. I replaced mine with a Pollack and have had no more issues. I'm sure there ae different brands out there, but Pollock seems to mate well with just about everything.
2013 F250 XLT
I now have a Keystone Outback, but I try to help when I can.
Bitter Gun Owner