My suspicion is that your coach may be wired to something other than today's industry standard which may account for the lack of functionality of at least some of your lights. Airstream utilized their own wiring process for the Bargman connector on the coach that can be found in the link below:
The industry standard to which most shops use to wire the Bargman connector today can be found in the link below:
If the shop that performed the work on your tow vehicle followed the practices that most in my area do when wiring a tow vehicle for a customer, the installation only inclueds six wires on the tow vehicle side as they don't wire the backup light circuit unless specifically asked to do so by the customer. My Airstream dealer wired the backup light circuit without prompting when setting up my '75 Cadillac and '99 Suburban for towing duty, but the independent shop that set up my '95 Chevrolet Z71 didn't connect the backup light circuit and wouldn't have provided the charge circuit if I hadn't specifically asked for the service (there was also an up-charge over their posted price list for adding the charge circuit to the basic 7-pin installation).
Also, if the coach is new to you or has been sitting for a prolonged period of time, you may want to disassemble the coach's Bargman connector for cleaning of the contacts. Even with just a few months of winter storage, both Bargman connectors (tow vehicle and coach) needed to be cleaned when I took my Minuet out of storage three days ago.
Good luck in finding the gremlin(s) causing the electrical issues with your tow vehicle/coach.