Not sure I understand clearly your wiring. However, if your coach has seperate brake and turn signal lamps and circuits, do you have a converter wired into your system for the dolly's lights? If so, I would certainly make sure it is operating as designed. Check power going in and going out. The less expensive ones have lower amperage capability and, if overloaded, will go away, sometimes one circuit at a time. And these things can do some funny things to the coach lighting when they expire. I would look there first....
Please let us know what you discover.....thanks!
2003 Fleetwood Revolution DP