The kill switch (7) is operated by the end of the governor spring lever (3) - see Page 28 of the workshop manual.
![[Linked Image]](https://www.outdoorking-forum.com.au/forum/uploads/usergals/2013/11/full-2772-13003-suzuki_m120x_kill_switch.png)
I suggest that you take a look at that mechanism, while operating the speed control from full to stop. I don't have one in front of me, but your engine should stop firing the instant the lever (3) pushes the switch (7). You may need to apply a resistance meter to the switch to establish how far it has to move to kill the ignition, so you can adjust it correctly without over-travelling and breaking the switch.
You might post a picture of two so we can all understand the adjustments.