"This morning the furnace acts in the same fashion as does the fridge"
Does that mean you can now hear the clicking from the furnace?
In our rig, the fridge and furnace won't light at first after a long time not being used, but the stove and WH light up ok. We have to keep trying and trying until the fridge and furnace finally light.
With the furnace it means using the thermostat to switch "off" let the fan stop and then switch "on" again. Fan comes on click and no heat. Eventually doing that it does light. Once it does it works fine for days, but same thing after sitting at home for a week or two.
There is something wrong with that--probably needs the burner cleaned, but I haven't attempted that yet.