As far as im aware if it has the stepped pin it should have a long rubber. Not sure if thats right, if the long one works i just use it. In you pic above the rubber would add some lenght. Without the rubber its got to travel further up the ramp to 'contact'
When the mower is off return the throttle to the middle. Thats the advice i give, saves the rubber.
Another major problem ive seen is the throttle cable length being setup wrong. Pop the hose off the bottom of the housing. Undo the adjustment screw and pull the plastic holder on the cable down out of the housing. Wind it like a nut down the cable outer if the throttle is cutting out too early (in or close to the start position) or you can not get full song (check with the cover off the carb that its rotating around fully).
If it wont stop wind it up the outer. Usually you can just adjust this with the external screw.
I would assume if you have to do the above that something has happened over time or it has just never been right. I have had a couple it i have had to bin because the plastic holder was not gripping on the outer of the cable.
