I've been poking around under the hood of my CJ-7 under the pretense of giving it a tuneup. One issue that I had noticed previously is that the vacuum hose that controls the flap in the air cleaner 'snorkel' had been cut and I have been looking for the other end of it. Well, looks like I found something today:
Better look here, with the arrow pointing to the cut-off vacuum hose:
Is this the connector for the air cleaner snorkel vacuum motor by any chance? At the moment the hose is open to the atmosphere which can't be good anyway but before I hook up the vacuum motor there I figured I'll ask here before I break something else.
Speaking of said vacuum motor, the intake snorklel looked like it was twisted for some odd reason, but some percussive maintenance got it back into a shape where the flap would actually move again without binding.
Guess I got myself another project 
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do you live where this has to pass emissions? If not then I would just plug that hose and make sure that the snorkel stays open (wire?). It may take it a bit longer to warm up that way but it isn't going to run well until warm with that Motorcraft carb anyway. I would convert that carb to a manual choke too
Not at the moment, but the CA border is a little more than a stone's throw from here and if I were to sell it, intact emissions gear would be a major bonus. Especially because everything is still there.
The electric choke works fine on the carb, the main issue I'm encountering is that it needs warming up before you can set off in really cold temperatures.
The snorkel is wide open towards the 'cold' feed, it would be nice if we could get it working as intended, given that it looks like all that's required for that would be the missing vacuum hose.
Must be a reason it was disconnected, maybe not. Did you test the thermostatic switch and the vacuum motor for operation under vacuum?
I didn't test the switch (I haven't really got much of an idea how) but I know the motor will hold the flap partially open.
I'm not sure about the 'there must be a reason'. if it was the same person who did some of the "additions" to the electrics I don't think I want to know about the reason 
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Actually with the damage snorkel, the flap wasn't moving freely so I wouldn't be too surprised if someone disconnected the motor instead of banging on the snorkel with a rubber hammer for a few minutes to get it back into the right shape.
There should be a emission system / vacuum hose routing diagram in the engine compartment, if not a manual, jeep sites or google search. On older models much of that stuff is probably disconnected, inoperable or goners anyway.
In general terms, not necessarily AMCs, for bare bones operation all you really need is manifold vacuum to the thermostatic switch (which usually have 2-4 ports). If the flap door is normally open (non-running), find the port on the TS that has vacuum on it w/ engine running(cold). That will close the flap by vacuum at start up and open when engine (coolant) reaches operating temp. If the flap is normally closed find the TS port w/ vacuum open when engine reaches operating temp. That will keep the flap open after engine is warm. There's other components like check valves, delays etc not necessarily needed but draw a diagram of whatever you remove. I don't generally mess w/ any vacuum lines/ switches to the distributor.
Test the vacuum motor w/ hand held vacuum pump like Mighty Vac. If it leaks down the motor is bad, a leaker may still work but w/ a loss of engine vacuum, not good. If the flap is designed to open full, engine vacuum should open it full. Oil the pivots on the flap too. Not sure of replacement parts for these anymore, I've owned a few AMCs but it's been years since I messed w/ 'em.
