Does it smell like anti-freeze (coolant) when you turn on the HVAC fan (are you running anti-freeze or just plain water in the radiator)? Are you loosing coolant?
Does the cabin seem musty/humid after a hard rain?
Check for signs of water leaks into the cabin, wet carpets in the footwells, stains, etc. (has the windshield ever been replaced?)
While you're at it, clean the inside of the windshield well with a good glass cleaner (Windex).
Would need to confirm further (coolant smell, coolant loss etc) but that sounds like a classic sign of leaking heater core based on symptoms. “Greasy film” is really the giveaway in my experience, though I’ve never specifically dealt with it on an 80. In other vehicles, the additional symptoms are things like damp passenger floor, etc, depending on location of the HC
I live in the Tongass rainforest and on occasion will get a quick light fog at startup (not a residue) when it’s been sitting overnight, but quickly goes away. I have accidentally been on recirculate a couple times in very humid weather and had light fogging around the edges of windshield, but goes away after I switch back to fresh air.
There is a strange smell - could be coolant but I'm not familiar enough with the smells to say it is coolant. Not too unpleasant, just a smell.
I use the truck in south Texas (Corpus Christi area), park inside at the house and at work. Have driven in the rain but never had any wet floorboards afterwards. Couple years ago when I had the truck in Houston I did notice wet floorboard on the passenger side but let it dry out and have pretty much parked inside since then so haven't had any more wet floorboards. At that time I had it parked nose up in a sloped driveway in a hard rain. I did the bicycle inner tube fix on the sunroof to hopefully tighten up the fit/seal there but haven't put it to real test. After I wash the truck in the driveway with a hose I do not find any wet floorboards or other areas.
There is no dank, musty smell in the vehicle after sitting. I have noticed a musty smell when turning on the a/c but have been attributing that to needing to pull the system out and clean it. Because of the way and location I use the truck I very rarely turn on the a/c or heat. Don't have much call for heat and when I'm driving it I'm usually conversing with various personnel outside the truck so I'd just be rolling windows up, down, up, down a million times. So I just keep them down.
I do have the stain shown in the pic. It's not wet and hasn't been wet in the last couple years that I know of. When I run my hand over the carpet in the passenger footwell it feels as though it is coated with some sort of fabric softener or weatherproofing product (kinda waxy feeling I guess). Could that be that it has just been soaked with coolant at some point in the past? Is this stain in a place indicative of a leak in the heater core?
I run the 50/50 Toyota red coolant and I do have to top up the reservoir (from the low to the full line) once every couple months. Not something that has concerned me.
The windshield has not been replaced that I know of (not in the last 90k miles that I've owned it and I found no evidence of it in the records from the POs). But it does have a crack all the way across at about the level of the resting windshield wipers. Been that way for 3 or 4 years that I recall.
I thought the heater core was essentially a "small radiator" that hot coolant runs through and when you ask for hot air in the cabin it blows air over the heater core to heat it. Are you saying that a leak means there is coolant on the outside of the heater core and blowing across it is essentially blowing atomized coolant through the vents (whether they be heat vents or defrost vents)?
