If it is a 2-bbl Ford EBU or Holley 2100 carburetor, try this:
There is a choke cable mounting bracket with clamp on the rear passenger side. Loosen the slotted screw on the clamp (may need to hold the nut on the backside with a 3/8" wrench).
Now, loosen the screw on the choke actuating lever (where the cable goes thru the round brass clevis.
Next, push the choke control knob on the dashboard all the way in.
Then go back under the hood and push the choke butterfly in the carburator so that it is all the way open.
It may be necessary to pull the choke cable all the way out of the clevis and the clamp to straighten the end of the cable a little bit (but leave a little curve in it at the end). Now thread the cable back through the clamp and into the clevis. You should have a little bit of cable extending out of the brass clevis. Be sure that the choke butterfly is still fully open at this point.
Tighten the screw down at the brass clevis (just snug up good, no need to crush the cable end).
Tighten the cable clamp screw using your screwdriver and 3/8" wrench.
Important: Go push the dashboard choke knob all the back in, then go back and look at the choke butterfly. If the butterfly is not completely open (straight up), your cable housing is pushed thru the clamp too close to the choke actuator clevis.
You will need to loosen the clamp again and push the cable backward thru the clamp to allow more room for the cable end to protrude from the cable housing.
After adjusting, test again, until you have the choke butterfly fully open when the knob is pushed in all the way AND the choke butterfly should fully close when the knob is pulled out.
It's all about how the cable is positioned in the clamp, as well as which point on the cable end is fastened in the clevis.