I don't understand the second picture. I see a button which pushes another button located below it. I don't know what the object below the top button is. If it is the top of the carburetor, that could be a flood button. You would push it before cold-starting the engine, and hold it down until fuel came out somewhere, indicating you had succeeded in flooding it. Then you would switch on the ignition, set the speed control, and pull the start cord. However I do not understand the wire that attaches to a tag at the bottom of the upper button. I do not see how you would use it to stop the engine, since it seems to be permanently grounded.
The magneto does not really look like an electronic type. My first guess would be that there is a wire on the other side of it that goes into the space inside the flywheel, and there are points and condenser located there. The kill wire, if it has one, would come out from either the magneto or the under side of the flywheel and go to a switch that grounds it.
