As I asked before, if you have the original style Briggs engine with a "magneto" don't just blindly move the ignition "kill" wire around on the ignition switch terminals, 'cause as I wrote before, feeding battery voltage back into the mag ignition system is NOT a good thing.
In my experience with various small engine and garden tractors, if you have the correct ignition switch for a mag system and look closely at the back of it you will see a copper strap crimped against the metal switch housing and the other end riveted to a terminal on the backside of the switch.
Look at the photo below, your ignition switch may be different, or have more or less terminals, but if it's lacking a copper ground strip similar to the one labelled "ground" in the photo more than likely it's NOT what you need and is for a machine using "Kettering"/battery ignition. Another thing to look for is that the correct switch will likely have a "M" terminal, and that's where the "kill" wire from your engine Magneto should be connected.
If you could post a photo of the back of your switch, that would be GREAT.