Neal, you don't really say if you've checked for battery voltage at the truck
socket. Some trucks require the installation of a fuse in order to make the
battery lead "hot" at the socket.
While the trailer battery probably won't get much of a charge from the
truck it definitely should power the lights in the trailer if the trailer battery
is low. I've plugged my truck back in many times to carry on when my
trailer was getting low.
Take a look her to see which pin is ground and which is 12v plus--