If i remember correctly, only the first stage is opened by the cable and linkage. There is a cam on the linkage preventing the second throat from opening at small throttle openings, but the actual opening is done by a vacuum-driven diaphragm bolted to the rear side of the carb.
You need to check that the tubes going to that are in good nick and correctly connected, and that this diaphragm is not damaged.
Remove it, stroke it, put your finger on the tube. If it gradually returns to rest position, the diaphragm is leaking.
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