Since Chevy's tend to run "HOT" electrically (high voltage) it SHOULD be charging. Several suggestions
First is there a fuse between plug and battery on Trailer?
Second. Inspect all wires.. To do this use not a volt meter but a TEST LIGHT You can buy one at any Auto place. (looks like an ice pick with a wire) or you can make one..
Bright light is good. DIM or NO light after the volt meter shows voltage indicates a bad connection or bad wire.
Check both Truck and Trailer YOu should have voltage full time on the trailer on the proper pin.. Just to the side of the index as I recall. On the truck when it is running.
