1966 Barracuda Formula S Choke ?

Has your intake manifold been off the motor lately ? If so, was the exhaust crossover passage open ? If its clogged with carbon (which happens very very often) the choke wont work because the exhaust gasses are not flowing through there to heat the bimetallic spring. The type of choke you have is called a divorced choke, some have an electric heating element in them and others do not, yours does not and relies solely on the exhaust flow through the crossover in the manifold. Try the adjustment suggested above, if it does not help then the problem is very likely the issue I described here.