Clearly, the evaporator is in the engine bay
But I don’t see any heater hoses going into the evaporator housing
Which makes me think the heater core is inside the car, under/inside the dash
I’m pretty sure the heater core is under the dash behind the heater housing, but get a manual. Leave that plastic housing alone. I had a 72 Continental that the wife drove that my neighbor used to call it a pimpmobile. He drove little SAABS. Nice comfortable car.
Reminded me of the old Cannon TV series. I think he drove one like it. Frank Cannon/William Conrad Private eye.
@OldcarsRbest, @db4690, @bing,
I can’t take a better picture right now, but at the very far-right of the housing is where the two hoses go in, and when i get my hand between the housing and the firewall, I can feel the heater core.
The Haynes manual instructions are completely wrong as far as I can tell. They have pictures that go along with the instructions that are not even remotely similar to the setup my car has, and the ford service manuals have nothing about replacing the heater core in my car.
I also took off the top of the dash, and the heater core is not accessible. There is a large plastic shroud that seems to run the width of the car (or at least half of it) that hides the heater core from the inside of the car, and I started to try to take it off, but there are so many things connected to it and so many bolts that I abandoned that idea, since it seems that the core is accessible behind the evaporator shroud.
I have all but one of the bolts out of the shroud, but the last one seems to go through the firewall (like some of the others), but I can’t seem to find it.
Bet you’re using some choice words about now! I feel your frustration, believe me. To access the core, you need to come at it from under the dash on the passenger side. There may be a ‘blend box’ with doors to direct air here or there; maybe a couple shift/speedometer type cables hooked to it, which will need removed. On the last one I replaced, there was one screw/bolt being retained with a speed nut (flat piece of spring steel with a threaded cutout) which I could not get to, so I used a dental pick to pry it off of the screw.
@OldcarsRbest Haha you have no idea 
. I took these picture of under the dash and behind the glovebox. Am I looking in the right place?
Holy expletive batman! Yes, that’s where you need to be. Has a few more gadgets hooked to it than the last one I did. Diagram and photo as you go to aid in reassembly. You know where it’s located (you mentioned you could feel it from the outside), now you just need to remove all the obstacles. Good luck!