Gents
This cable often becomes faulty when the end remote from the pump i.e. at
the diaphragm end has the outer pulled into the cable adjuster and therefore
the idling adjustment is nolonger operated when the engine vacuum changes.
Worth a check first there. There is not very much movement on this cable
when it is adjusted correctly. Check the movement by looking at the cable
travel  behind the pump where the two idle adjustment screws are located.
Mike