OK, so no big problem anyway! So the issue left is that you do have 13.8 at the truck's 7-pin so pin #4 (charge line) and the ground pin there are ok there.
The trailer battery voltage is reaching the end of its 7-pin cord connector too, so no breaks back from that.
That leaves the actual connection in the two 7-pin connectors not making contact. You can scrape them inside with a screwdriver or knife, and wiggle them until you get good contact.
Outside chance is on a poor wire you can get the proper voltage with your meter, but it cant carry any amps, so you could have a bad wire connection inside the back of the 7-pin (either one) where the wires screw down on their pins. Those connectors come apart so you can get at that.
If you had truck power to the battery, but the battery disconnect open, it still would not run the lights, but the trailer battery voltage would go up.