Assuming you are working with a "stock" motor. Make sure that your exhaust crossover passages are open as their heat is required for the choke to function. I will try to walk you through this but a copy of the factory service manual would be very helpful You can download a copy at LINKY
1.Take the air cleaner assy. off and allow the motor to sit to cool down (preferably overnite)
2. Once cool, Block the primary throttle arm open 1/4" or so.
3. The choke butterfly should snap shut completely and have a slight spring tension when trying to open with your index finger.
4. If it does not close with tension the thermostatic spring or arm needs adjusting. (I'm not sure which is used for adjusting on your particular application) The amount of tension determines how long the choke stays engaged. (warmer temps require less tension as the motors warn up quicker).


The next 2 adjustments (A, B & C ) are interrelated and where the confusion with setting them up properly comes in.
1. Remove the apparatus holding the primary throttle open.
2. Give it a 2 or 3 pumps, ( may require more). Have a helper ready to cover the carb with a wet towel should it stack fire while Starting the motor.

Now for the interrelated adjustments. (can be confusing)
Once the motor starts, The choke pull off (vacuum operated) should open the choke enough ( usually about 1/4" or so gap) to allow enough air in while keeping the fast idle cam engaged and the motor idling at about 12-1500 RPM.

A. if it is running rough and loading up, try blipping the throttle, if it continues to load up, either the choke butterfly needs to be opened more (adjust the pull off slightly) or the fast idle speed needs to be lowered.
B. If it is idling to high,"blip the pedal once to see if it drops, If not, be prepared to shut it off as the "fast idle" is set too high, lower the setting.
C. If it won't stay running the fast idle needs adjusting, again shut it off and raise the fast idle speed


The three steps above A,B, & C affect each other so it is a balancing act between the Three to accomplish proper choke operation. Keep in mind the 1st section controls how long the choke stays on.
The factory manual will have recommended procedures and measurements to achieve the above. Their recommended adjustments will usually get you pretty close
Final testing needs to be done on a cold motor.
They are quite simple once you understand the various adjustments. The difficulty is getting all 3 where you want them and the fact that once the motor starts to warm up even a little you need wait until it is stone cold to proceed.

have fun

I have bee able to make them work with blocked off passages by loosening the initial spring tension and just using the engine heat for the thermo spring but it can become a bit more challenging and possibly require more pumping of the accelerator pedal to enrichen the mixture enough for the initial start.

The choke doesn’t seem to be closing at all on a cold engine. What do I need to adjust to get it to fall closed once the accelerator is pumped on a cold engine?

Some of the chokes are adjustable by loosening a screw on the thermostatic coil mounting post, rotating it, and tightening the screw back down. The choke should be removed to determine which you have as it may have been replaced with an aftermarket unit.

Others are only adjustable by bending the rod between the TS coil and choke butterfly.
Or as Nitrous mentioned you may have the wrong choke / rod