You have what is known as a "sail" and a "sail switch" in your furnace and it sounds as if the sail itself may be stuck or the switch may be bad. The sail is basically a small piece of light sheet metal which moves, as a boat sail, when the furnace fan moves air and the movement of the sail makes the sail switch tell the circuit board that the furnace fan is moving air. When the furnace initially lights up then it will satisfy the thermocouple telling the circuit board that the burner is on and producing an appropriate amount of heated air. Within seconds the fan comes on to blow the air into the heating ductwork. This is when the sail is moved to activate the sail switch itself. With the gas and electrical power turned OFF you will need to look into the interior of your furnace to find the sail. Once you find the sail you will readily find the sail switch. You may even have to remove the furnace from you RV to work on it. IF the sail is hard to move you can use just a drop or two of oil at the pivot points to lubricate the sail. IF the sail appears to move freely then you will need to check the sail switch with an Ohm meter to assure that it is working properly. This type situation usually happens to furnaces that have sat for some length or time, such as months, in high humidity atmospheres causing the sails pivot points to sort of lightly rust over causing too much friction at the pivot points.
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