The B&S governor on those relatively early engines had an air vane connected by a wire to a pivoted link. The pivoted link was connected by a spring to the speed control. Another wire connected the pivoted link to the throttle butterfly. The force from the air vane was balanced by the force from the speed control spring, so the position of the link moved back and forth depending whether there was more force from the air vane or the speed control spring. The throttle butterfly simply mirrored the position of the pivoted link, since it was connected to it by a rigid wire. What this meant in practical terms was that there was always a rigid wire connecting the throttle butterfly to the governor. In your original picture the arrangement was approximately correct but the governor spring may have needed to be connected to the hole directly below the speed control cable - most likely it won't make much difference since it is still attached to the same bell crank. The original problem you described sounds as if the governor may have been hunting. This can be due to something wrong with the governor, but more often it is just lean mixture. Try adjusting the mixture screw a bit less than a quarter turn anticlockwise.
