So here we have a G3 carby (not one of my strong points, anyway the pin can get dirty and stiff to move (little brass bit that the throttle cable connects to) that can be cleaned, I would suggest against trying to disassemble it though, the plastic would be getting close to 40 years old and probably getting a little brittle, some compressed air and some sort of lubricating spray may help though.
The pin when you push the throttle to the stop position gets pushed in a little bit to make contact with the brass part that the little black wire (pictured) connects to, if the pin gets stiff in its holder it may no longer make contact.
Alterntaely if that is not the issue the throttle cable may be out of adjustment, not allowing enough pressure be applied to the kill switch.

joe.