This should be an easy one!
Look for the vacuum reservoir which is probably located on an inner fender shield under the hood and may be a plastic ball but more likely just like a large can used for food painted black and one hose to it. The bracket that mounts the thing frequently rusts at the bracket and leaks. If you pull off the vacuum line (carefully as to not break the plastic part at the reservoir) it should be holding vacuum and go whooosh.
If it doesn't it isn't holding vacuum in reserve for the times when engine vacuum drop such as when you described.
TMK - if that's it what I do is take the metal ones apart clean up the rusted spots and use liquid electrical tape which is a brush-in-can neoprene that will seal it, tolerates fuel and oil, and can be painted. These are not available new but a generic ball can be found but you have to be creative to mount it. The holding nuts are 9mm on the inside of the fender shield and will frequenty break off. If you have the time let them break, with the bracket removed (bend the four tangs open it will realease it) and drill out old ones and you can fuss to replace them or just use a good long wire tie thru it and the fender well to attach it.
If too rusted you will have to give up on that one. It's better to just plug off that vacuum line then let it keep leaking till you can find a replacement.
There are two sizes of the metal ones. Just measured the smaller one that I keep on hand which is about 3.5 inches long and will replace the larger one and work properly but you may need to drill another hole in plastic fender shield for the mounting studs.
If you can't fix or find a replacement hit me with a PM and I'll sell you mine at cost of shipping it.
Do replace any vacuum hose which is generic by the foot and i.d. and best to take an exacto knife and cut old ones off and peel them off because broken plastic spuds really can't be glued back on.
There is also an inline check valve that can be purchased new if broken. I have those too
Keep at it. This is a common problem for the vintage,
T
Tom Greenleaf - MetroWest Boston - USA
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http://www.autoacsystems.com/tomgreenleaf/