Well there is a lot missing info here. This is like saying I have a engine that I what to put in a Ford pickup.
Got know the keyswitch PN , got the have the engine model and type numbers, and need equipment model numbers that that you are trying to rewire. We also got to know what alternate if present you have on the Briggs engine.
I can't help this time other than having the schematic , but make it easy for next time . Keep a few colors of nail polish handy and before disconnecting anything apply a color to each connection .