Pulling the wire off and having it then start means everything upstream from that point needs checking to find a possible short to earth on the kill wire. With the cowl off move the throttle linkage and determine how the kill feature works on that particular engine. You could probably tell how it is supposed to work from the manual you downloaded. Many just have the full off position making contact with the kill wire to earth it. Follow the green wire to see where it goes and see if you can find any place it has worn through or if there is a stray strand touching somewhere at the end.
As to the self propelled, sorry, can't help there.
