As a much younger man, I got the name tag that said "Trailer Service Manager" only because I could sleuth out the bad ground problems endemic to trailer lights.
Excuse the short clarification here, but are you getting the same results from two different tow vehicles or from two different trailers...
It reads as you have the same situation with two different trailers..
Trailers should be wired so that the tail and marker lights all come on with the tow vehicles parking lights. If that is not what you are getting, the use a test light to probe the trailer connection in the tow vehicle.
Matt
Matt & Mary Colie
A sailor, his bride and their black dogs (one dear dog is waiting for us at the bridge) going to see some dry places that have Geocaches in a coach made the year we married.