have had trouble with the converter plug at times, is a head scratcher too, usually just clean the terminals and it works again...or at times it will blow a fuse under the hood. just don't trust it.
as far as just an extension, if it is wired the same as the truck and trailer, it should be grounded and work, SHOULD is the key word here.
I'm with nihsif on checking to see if they are wired the same.
good luck, let us know what you find out, may have the same problem at some point.
6 years ago I put LED tail lights on the trailer and have not had a problem....do periodically do a quick clean of the connection is all, they are double sealed so I don't unplug them to back in.
imagine now that I was bragging about that, they will quit working tomorrow