1966 Barracuda Formula S Choke ?

It's uses heat off the exhaust crossover to heat the bimetal spring type choke. They are fairly simple but all the components need to function for it to work properly. First, reattach the choke rod to the choke flap. Then open the throttle and see if the flap closes all the way with just a little pressure keeping it closed. Pull back in the choke pull-off rod and adjust it (by bending) so that it opens the flap about 3/16" or so. Start the engine and see if that adjustment will allow the engine to run smoothly. If not, adjust the pull-off rod until it does. If the choke stays on too long or won't completely open when the engine is hot, the exhaust crossover passage in the intake is probably clogged. You'll need to remove the intake and have the carbon/burnt oil buildup removed. I usually start with a small chisel to get the big stuff and carb cleaner or the sand blaster the get the deep stuff. Run a coat hanger all the way through to make sure the passageway is clear. There is an adjustment on the choke itself but unless someone has messed with it, that won't need changing. You'll have to look in the factory book to get the exact setting depending on your particular application.
Have fun! Mark