We may not have progressed very far, because you only posted pictures of the carburetor and linkage with the speed control in the fast position, not the slow position. However, your engine appears to have the Dellorto carburetor - see this drawing from the Tecumseh workshop manual:
![[Linked Image]](https://www.outdoorking-forum.com.au/forum/uploads/usergals/2012/10/full-2772-8602-tecumseh_tvs_dellorto_carb.png)
The red circle encloses the throttle butterfly bell crank. The only component connected to the bell crank on that engine is the governor link. and on your engine the link has successfully opened the throttle butterfly wide open in your picture:
![[Linked Image]](https://www.outdoorking-forum.com.au/forum/uploads/usergals/2012/10/full-2772-8603-tecumseh_tvs_dellorto_carb2.png)
The red circle shows the venturi area in the bore of your carburetor. You are looking at the throttle butterfly on its brass pivot shaft. The throttle is edge-on, meaning it is wide open. If you pull the governor arm (at the right of the picture, where the rightmost green arrow points, with the governor spring and the governor link connected to holes at the top of it) gently toward you so that you stretch the governor spring slightly more, you will see the throttle butterfly close to the idle position, obstructing the bore and preventing the engine from drawing in much air. When you release the governor arm, it will snap back to the wide open throttle position, due to the force of the governor spring.
The two green arrows show the two ends of the governor link. It runs from the top of the governor arm, to the bell-crank on the throttle butterfly.
The governor spring runs from near the top of the governor arm, to the speed control lever circled in red in this picture:
The speed control cable from the handlebar connects to this speed control lever and sets its position. The governor spring also connects to it. When you move the lever on the handlebar toward fast, the cable moves the speed control lever and stretches the governor spring.
Now, I suggest that you watch the speed control lever, the governor spring, and the throttle butterfly inside the carburetor, while you move the handlebar lever. You should see the butterfly almost closed at the idle position, and wide open at the fast position. This indicates that the mechanism is working correctly. It may or may not need precise adjustment to get the prescribed speed settings for idle and maximum speed.
Incidentally when you removed the two vertical screws that hold the top plate of the mechanism, you destroyed the alignment of the linkage, so it will now have to be set up again with correct alignment.