pull the blower housing off and check where the wires go.
You should have one going to the carb which needs battery voltage while the engine is running
There should be one going to the coil which is the kill wire and goes to ground to stop he engine ( open circuit to start )
After that you are left with the alternator wires.
These are problematic because there is a dozen different alternators that could be fitted to that engine .
For those you will either need to start the engine then see what comes out or get the IPL for the mower it came from.
If there is a piggy back solenoid like a car then yes the battery cable goes to the solenoid and you will have to fit a monemtry switch to go the the trip terminal that gets 12V to start.
I have a 18hp Vanguard engine I am using as a repower on my walk behind. I have the engine mounted fuel ran etc. My question is how do I set it up to start. My walk behind was originally a pull start and this engine is electric start. I already have a battery, I assume I wire the main + lead to the bottom of the solenoid just like a car. There is a small harness coming off the engine I have a picture of. I just want to hook the on-off to a toggle and starter to a HD push switch. I have searched but cant find a clear answer