One of the bonuses of rebuilding/resealing the heater box is you can also pressure test and clean the AC coil. I redid mine about two years ago and was able to leave the coil under vacuum for a couple of days to test it at home. If it’s holding freon it should be okay, but sometimes they get bumped and dinged upon removal and you don’t want to find out it’s bad after you pull, rebuild, and reinstall all that. FWIW, mine had a small mouse nest in the fresh air opening, but it had several shed snake skins in the ac coil, which explained why I had no continued rodent damage. Point being: you kever know what you’ll find in that box, and it might be a pain but it’s really worth it to pull it and redo it.
Additionally, I had a vacuum can in the fender that was rusted through and lines that were bad. So, I replaced all the old vacuum lines with new ones, cut the top off the old can and used it for a correct facade, and then used a newer round vacuum pod from an F150 inside the inner fender to sidestep the poor quality of repros. I did a similar deal with the headlight door vacuum tank which was also in poor condition. I checked the vacuum motors on the hvac box with a hand pump and had to replace one that was bad.
The vacuum actuated stuff is a whole system. I wasn’t keen on running an electric or engine powered vacuum pump, so when I selected a new cam I made sure I was going to pull at least 15 inches of vacuum. A lot of Cougar owners who hop up their cars wind up realizing too late they don’t have sufficient vacuum to run the hvac, headlights, and brakes because we are now in the age of lopey cams that EFI tends to bandaid. But you can get an electric vacuum pump to run the entire system independent of engine vacuum if you want a lopey cam.
The systemwide test can be done by pulling the vacuum line from the carb or spacer, pulling a vacuum on it, and seeing if it holds, how long it takes to leak down, how long it takes to pull the headlight doors shut, and how long the doors stay down. Any leaks will impact the heat control valve, hvac doors, and even power brakes in large or small ways. This will make the AC temp warm, the vents not operate properly, and generally have poor function instead of the snappy way they should work with a slight hissing noise. These were OP’s complaints.