The divorced choke simply pushes the choke linkage up to close the flap when the engine is cold. When the coil heats up, it pulls down on the choke linkage and allows the flap to open. There is some adjustment by bending the link between the divorced choke and the carburetor.
The picture shows a pretty steep angle between the choke coil and the carburetor, in most cases the choke is directly under the carb. Could be binding up when applied. I'd check choke function with the link unhooked, then verify it can move it's full range of motion with the link hooked up.
Also verify that the coil is working in the right direction cold and when it's heated up. Also a bit old school, and some bending of parts is required for adjustments, those types of chokes work flawlessly when correctly adjusted....Cliff