To properly wire and configure your Furrion Chill Cube Ducted RV Rooftop Air Conditioner Single-Zone Wall Thermostat for controlling your Suburban furnace, follow these steps:

1. Identify the furnace control wires, typically two brown wires labeled "FURN" on the ceiling controller.
2. Connect these two brown furnace wires to the Suburban furnace's 12V+ and ground terminals. The polarity is not critical; either brown wire can connect to either terminal, but ensure the connections are secure.
3. Set DIP switch #2 on the thermostat’s control box PCB to the ON position to enable furnace control. If you change DIP switch settings, power cycle the unit to apply changes.
4. Verify that the wall thermostat is connected correctly to the control box using the provided 4-wire harness with matched colors.
5. Restore power and test the system to confirm that the thermostat controls both the air conditioner and furnace properly.

If you did not receive or use the specific adapter that comes with the thermostat, ensure you have it connected as it is necessary for proper operation. Following these steps should resolve the issue with your furnace not powering on through the thermostat.