Hi Josh, welcome to Outdoorking.

The engine just has a kill wire, a pair of alternator output wires, and a terminal on the starter to connect the heavy wire. The more significant wiring is almost entirely on the mower, not the engine.

There are two standard designs for the mower wiring recommended by Briggs. The difference between them is that one uses a 5 terminal starter switch, and the other a 6 terminal. Here are the diagrams:

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