It sounds as though the indicator is the only thing that is malfunctioning on your auto regulator since you have good flow to the stove. While the furnace may require a higher flow of propane, I doubt that the regulator is the issue here. We still do not know if the changeover function works. May want to replace it.
I am not an expert on furnaces so someone else may have to chime in. There is a sail switch that has to come on for the flow of propane to start. This detects air flow. In a rig as old as yours, these can fail or get so dirty that they don't work right. Also be sure the exhaust is not plugged with wasp nests etc. I think that would be a good start.