Choke assembly on Briggs Spirit 375?

Hi, I have a Hayter Hawk with a B&S Spirit 375, which is running rough (revs from medium to low intermittently but does not cut out). Both my local service centres have a 6 week wait time so I have tried the following myself. New spark plug, new oil, fresh petrol, cleaned and re-oiled air filter. This is the limit to my "service" capabilities. on removing the air filter I ran the mower to view the choke assemble below. as it revs from low to medium the butterfly choke and the arm, to which it is linked, move as the engine revs up and down. My question is is this movement causing the reving? or is there another cause to the revving which results in the movement?The butterfly part and the arm are connected by a solid pin, The idle Govenor spring runs from the loop on the solid pin to a static loop towards the front. the main govenor spring runs from the manual choke adjuster to the same loop in the solid pin. Moving the manual choke has little if no effect on how fast the engine runs, all it does is very slightly add tension to the main govenor spring but not sure this does much. Is this setup correct? Is a part missing? something more solid between the manual choke adjuster and the butterfly choke or arm to which this is connected? I have a photo of the assembly which I can send if it helps. Hayter Hawk manual and Briggs 375 manual do not help. thanks Nish