I puzzled over that since it is a little bit backwards. What I would actually surmise is that there is a vacuum line that split someplace and leaks only under relatively high vacuum - as in when the throttle snaps closed.
Low coolant doesn’t fit either if it cools “swiftly.” I guess it depends on how swiftly it cools. Even if the heater core isn’t being fed enough hot coolant, or if it is restricted, the effect won’t be “swift” - it would be gradual. The problem apparently didn’t change after cooling system service either. Perhaps the OP might return at some point and provide more complete info. Or perhaps this will be yet another thread where the OP never returns.