Check all vacuum hoses for cracks leading to leaks, or hoses having fallen off. However, I'm quite sure you have a vacuum motor out. These are the bulbous looking canisters that are actuated by vacuum, and if the rubber badder (bellows) starts leaking due to age cracking, you'll have the symptoms you described. These motors have really small hoses attached to them, fed by a hose from the engine bay to your on/off switch and then to those motors. They can be checked with a Mighty-Vac, or just suck on them really hard. You should see good movement by the small arm that sticks out from the motor. I've tested them up to 25 pounds, both vacuum and applied pressure. There should be 3, maybe 4 of those motors, all under the dash and attached to the heater core housing.
The check valve is built into the vacuum canister. It is mounted on the outside of the psg rear apron. The valve sticks through a hole just under the hood hinge. Check the canister as they do rust out.
Mine does the same thing, a 68 XR7. I found mine was missing the vacuum can that is supposed to be mounted in passenger fender. I just ordered a new can from Classic Auto Air, they are also available from WCCC. Bought mine from Classic Auto Air because they sold me the updated A.C. Components under the hood ( compressor, hoses, evaporated, basically everything under the hood). I believe that to be my issue, that could be yours too. Leaking hoses can do it too. I think you can usually hear them hissing if there is a leak just after you shut off the engine. Hope this helps.
One way valve in AC reservoir canister was bad. Instead of replacing this $100 can, simply placed a universal one way vacuum valve in-line $5. Unit works great. Guess my car will never be concours........