The choke on the 1946 can be confusing, I know. It works like this:
There is a hot-air line for the choke housing that MUST work or else the choke will delay opening for a very long time. You've already noticed this. It works this way: the heater element is a variable-resistance- device that becomes very high resistance (like an open switch) below 60 degrees. Above 60 degrees, it drops to below 100 ohms, drawing about 1/4 Amp from the 7-volt tap on the alternator (Fairmont/Zephyr alternators have a 1/2 BATT tap on the back of them for this). After it reaches about 90 degrees temperature, the heater drops resistance to about 10 ohms.
The lower the resistance, the more current it draws and the hotter it gets, opening up the coil as it gets hotter. BUT-you have to 'get it started' with the warm air first.
Now, here's the hard part - in the Fairmont/Zephyr exhaust manifolds, there was a little 3-turn coil of tubing inside of the manifold. One end of this coil of tubing connected to a flange-mounted port on the 1946 (on the passenger side of the installed carb). This supplied filtered cool air to the tube. The other end of the coil went to the choke housing to bring the hot air in and warm up the variable-resistance heater element in there. A small passage near the top right of the choke housing goes directly to the bottom side of the carb flange to provide the vacuum to pull this warm air thru the choke.
Now, during the 1980's, there was a lot of MTBE in our gasoline, which becomes acid at exhaust temps. This ate away the little coils, which then introduced raw exhaust gases into the choke housing and the cool-air flange on the 1946, often destroying both ends of the carb, then warping the top plate of the carb from the extra heat.
The solution to this whole thing is to get some of that soft aluminum tubing (Checker sells it in their "Choke Heater Rebuild kits" from HELP! parts). Buy 3 kits, and also get two 1/4" compression unions for copper pipe from Home Depot or Ace Hardware. Connect all 3 aluminum tubes together, then slide a coat hanger wire (all straightened out, of course) down the center. Wrap the tubing around the exhaust manifold at least 3 times, then slide the hanger wire out of it (the wire keeps the tubing from pinching shut). Connect one end of the tubing to the choke housing and the other end to the cool-air port on the carb's flange. It will then work just like you thought it should!