Suburban furnace SF-30F serial#940804195

With everything in place. Bang on the furnace housing when the furnace first comes on. THAT will cause a marginal Sail switch to usually close and fire. IF that fixes it, replace the sail switch, and/or check the mounting of the "sail" of the sail switch. You really need to post the EXACT digital dc voltage of the power at the furnace when running on 12 volts. You may have good voltage at the RV ,but is it the same at the furnace? The difference between shore and battery is simple---the shore power converter is putting out a higher dc voltage (maybe only 1 to 1.2 volts) but THAT is enough to turn the Fan motor at a faster RPM. If the sail switch is defective or is sticking, that faster RPM is overcoming that problem. Also, CLEAR and OPEN heat ducts are required. There is a Case(Static) pressure on furnaces. If that pressure is to high (inadequate number of heat ducts or partially blocked ducts) that will cause the motor impellor to not supply enough force to close a sail switch, especially on battery. That may be why you remove the inside cover and it fires on battery. Doug