From the photo's I can see you have an ECG-5 carb. It's Ford, but made by Holley.
This carb does not have provision for automatic choke.
If it were me, I would find the choke cable bracket somewhere and get a choke cable kit to install in or under the dash.
Mikes Carburator Parts might have the choke cable bracket that goes on the carb. Just tell him you need one that fits any Holley 94. If they don't have it, ask CharleyNY, he might have one.
If it is a '56 intake manifold, there is a copper tube sticking up out of the left side of the intake for the choke housing connection. It that is broke off, it needs to be plugged. Look at how the distributor vacuum tubing is crimped where the rubber hose connection is. That could be a vacuum leak there. Cut off the tubing with a tubing cutter and put the hose back on.
CHECK your intake vacuum at the brass block in front of the carb. The vacuum reading should be 19 or better on the vacuum guage.