OK, So the two most common Issues I find that cause this are the kill mechanism, and the throttle cable.
Try cleaning out the throttle assembly, and that may help, as they fill up with muck, and can't connect properly.
However by this age, I usually find the throttle cable itself is not performing at peak, which means it can provide enough movement to give you most of the throttle range, however it just can't give enough pressure to connect the terminals.
I would suggest in this case, cleaning out the cut out very well, and making sure the contacts are clean, then when you want to stop it, apply pressure to the throttle control lever with one hand, while jiggling the throttle cable about 2" from the carby.
If that fails, stick your finger in, and push the kill switch, or the end of the cable (Hook).
As for replacing the cable, that's not always easy, they are no longer in production, so it's about finding stores with stock, or watching eBay.
I'm working on a restoration method for them, involving removing the inner cable, and replacing it with a similar wire, the hard part is replicating the twist at the end.
