[LMP]

You already have two 3.1/3.4 classic symptoms (no heat "at all" , fluctuating gauge) ....the third would be engine overheating..any sign of that yet? Remove radiator cap and start engine...look for bubbles escaping the radiator while someone else revs the engine in short surges... Head gasket failure is so common with these symptoms that it cannot be ignored as a real possibility....a very annoying and unwwanted possibility.
Can you peek under dash ..possibly remove glove box ..and see if you see or hear something move when you slide the temp control from cold to warm...(mixer door)..I'd rather want that blockage to be the cause, it has happened before.
Actual blockage of the heater core can be alleged...but rare.