Best thing to do is rip out all the wiring and make your own I do it often. Order a toggle and push button start. Maybe a new solonoid. It's most likely 12v it's tractors that need converted not lawnmowers.
It's easy and you'll learn a lot. The engine itself is very easy, it's all the other stuff like safeties etc that start turning the wiring into a rats nest. The engine will run independent, only thing it needs is turn the starter wired and turned over. It only has a hot wire the battery grounds to the frame. You do need that switch though lol. If it's a Briggs it will have a black ground that goes to your toggle. Then 2 wires for charging. Be easier to watch a vid. The guy in Fearlessfront explains all this and makes it easy. Just keep in mind the hot wire from the battery to the starter and the battery ground both have to be heavy gauge wires otherwise your wiring will spontaneous combust lol. All fine and dandy till the gas goes next then you have a fireball in your yard and it burns to a nice rusty color. Needless to say I've seen it happen lol.
https://www.google.com/search?clien...i71j0i13i30j0i8i13i30j33i21j30i10.0bShQAmJ_fE
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The fearless front vid is the first one, it's good. That guy builds really cool stuff.