A vacuum leak is one possibility, but I think not the most likely one here. Find and repair the exhaust leak near the middle of your exhaust manifold, and the problem will go away.
When you hook up that vacuum hose, the air cleaner's thermostatic sensor is cold, so it sends the vacuum along to the actuator in the air cleaner snorkel, which lifts the mode door up so the air is drawn through the flexible stovepipe which runs from the bottom of the snorkel to the sheetmetal heat stove surrounding the central collector part of the exhaust manifold. This does very good things for driveability/performance, fuel economy, and exhaust emissions before the engine is warmed up.
Exhaust leaking near that stove will be drawn into the engine, which will gag on it at idle and promptly stall, every time.
There's an outside chance the problem is a bad hotbox (intake-to-exhaust manifold) gasket. That would have to be a large leak, though, because that junction is above where most of the air is drawn into the stove. More likely your exhaust manifold is cracked, so you'll need a new one. That's the bad news. The good news is that replacing the manifold will solve
all possible causes of this kind of leak—cracks, worn out heat riser valve bushings, faulty hotbox gasket, etc—so you won't have to carry on chasing your tail about it. The other good news is that this fix will make the car a whole lot less hazardous to your health and safety; these cars were not very well sealed against entry of engine bay air into the passenger compartment even when they were new, and they don't age well in that respect. An underhood exhaust leak is very dangerous; even if not enough exhaust gets in the car to knock you unconscious, it only takes small amounts to dull your cognition and slow your reflexes—not what you need while driving.
Read
here about manifold selection;
here about manifold hardware;
here about manifold installation, and It is very much worth your while to get the
good gaskets for the manifolds-to-head and intake-to-exhaust junctions.
