My control is exacly like this and I repaired it very recently.
I could not engage the engine in my case.
These control housing are not watertight and are usually exposed to the weather.
They need to be lubricated with grease (I believe yearly).
The button attaches to a pinion with thee teeth that runs with the pinion from the speed lever.
The attachement is made with a small pin crossing the button.
The gear was excessivelly weared on the pin holes and the pin was slipping.
I turned the pinion around (it is simmetrical) and drilled new holes to receive the pin on the back face, greased everything, intalled a ruber gasket and closed it. It is working like when it was new.
Need to be careful with the two springs and the two spheres that hold the throttle button and the speed lever shaft.
