Automatic chokes are pretty simple devices. Inside the black bakolite choke housing on the side of your carburetor is a bimetallic helical spring. As the spring warms up the two differnet metals of the bimetallic spring expand at different rates, which makes the spring "unwind" a little. That rotates your carb choke plate to the open position.
The bimetallic springs in the original chokes on our old Chris Crafts were heated by exhaust manifold heat piped to the choke via a piece of copper tubing. As the engine started to warm up, the heat from the manifold rose up the copper tubing and heated the bimetallic choke spring, opening the choke.
Electric chokes do not use exhaust manifold heat to open the choke. Instead they simply have a small 12volt electric heating element inside that black bakolite choke housing. One side of that heating element is grounded to the negative side of your electrical system (normally to the engine block, but in your case it sounds like it is grounded to the carb body), and the other side needs to be hooked to a 12 volt source activated by your ignition key. When you turn your key on, the little electric heating element slowly begins heating the bimetallic choke spring -- it takes a couple of minutes for it to get hot enough to fully open the choke.
The + side of your coil is a 12v source controlled directly by your ignition key, so that is most likely where that red wire you mentioned went to.
There are three clamping screws holding the bakolite choke housing onto your carb. Look close and you will see calibration marks on the housing. Loosen the screws, and you can rotate the choke housing to control how rich or lean the choke will be when your engine is cold.
Best wishes, Curt...
1967 fiberglass 38' Chris Craft Commander Sportfisher with twin 427 CID 300 HP engines.