I can't see any electrical switches, so it's not a CA setup! That helps.
You have one of the more complex vacuum setups, but everything looks pretty well intact. That little round plastic and metal thing hanging out on the valve cover is a vacuum modulator. It provides a modified idle vacuum.
But what I think is the first thing I'd look at is the plumbing that goes down between the manifolds between the carb and the firewall. Since the older iron intakes didn't have the coolant passage, AMC mounted the thermal vacuum switches on the block way down low in some water jacket openings.
The front one is EGR, but the back one switches your distributor vacuum signal based on engine temperature. When the engine is cold it gets manifold vacuum to help cold driveability, then when warm it switches to the vacuum modulator.
There should be manifold vacuum to the outside port, the center port goes to the distributor, and the inner port goes to the modulator.
The modulator gets the ported vacuum signal from the carb and manifold vacuum. The plastic body should be marked, and the port marked distributor goes to the switch I just talked about.
The parts going down to these switches pass very near the exhaust manifold, and so the rubber cracks and the metal tubes can rust through. I suspect that you're getting a leak somewhere in that plumbing or the switch on the block.
You ought to be able to tell if the modulator is making noise since it's way up front away from everything else, but it may be the problem as well. It keeps the distributor partially advanced at idle then transitions to ported as the throttle opens, but things act normally under full throttle.
I think you may be on the right track with the advance hose, it's just all that spaghetti in between.
I can't really find a vacuum diagram specific to this. I don't have a TSM handy. 80-82 setups can be very different.
I hope all this is helpful.