It's a very simple system. The lever in the car pulls a solid wire inside a sleeve. The sleeve is held still by an arm on the carb, leaving the centre wire to pull the choke lever on the carb. A spring pulls the choke lever to the off position. Friction in the lever in the car holds it on. If there is too much friction anywhere along that length, the choke will stay on even if the lever in the car is pushed off. Similarly, the spring might not be pulling as hard as it once did.
Does the choke lever on the carb move freely with finger pressure? If you undo the clamp on the cable, does the choke lever spring back when you let go? Then the problem is with the cable somewhere.