Greetings Barry, and welcome to the Forum!
Gees this sounds perplexing ! Specially when "module" is used !
Are the Trailer Connections an after market install? Sounds like someone just messed up and got some wires shorted on your Light Connector for the Trailer.
Look at about the middle of the rear bumper, underneath it, and see if there's a taped or patched Connector added to your Tail/Brake lights.
If so, you can just remove it, and re-tape the wires separately, and see if that doesn't correct the problem.
Let us know what happens.
Have a good Day !
S.W.