The 2 blue wires on the suburban
1 Blue wire will be HOT (12 volt) all the time on MOST RV's. THIS wire goes to either the AC upper control board OR goes direct to Wall Tstat. Then depending on if going to the Wall Tstat, the other Blue wire will connect to a different color(usually) going to the wall tstat. When you call for Furnace the 2nd blue wire is closed to 12 volt with the original 12 volt blue wire at the tstat. This sends the 12 volt signal to the furnace to start a run cycle
IF the wiring goes to the Roof AC then the 2 blue wires go up to the Roof AC control board and the Furnace relay ON the Roof AC control board closes and sends that 12 volt signal to the Furnace to run.
Since it appears you have determined that the Furnace wiring goes to the Wall tstat, forget the AC control board.
The WHITE wire coming out of the wall tstat is connected to the Cold(Dead) blue wire at the furnace. Doug