Finbar, I can see in your new picture that your engine has a spring-loaded device to short the spark plug: the piece of steel sheet springs back when you stop pushing it against the top of the plug. I haven't personally seen one like that since Briggs' WW2 engines. At some point Briggs switched to using a generally-similar device made from aluminium, that pivoted where it mounted to the cylinder head. This meant that when you switched it off by snapping the piece of aluminium into its "down" position, it stayed there and the engine stayed switched off. This was likely to be safer if someone rotated the engine for some reason.
I don't know at this point whether the spring steel device was retrofitted to your engine, or it remained in use much longer than I thought.