First you want to use a relay, they are cheap and less likely to cause a short.
The "Push button" will CLOSE the relay so can actually be a Ground, so only 1 wire needs to be run to this "button".
On the ignition switch there will be a Pink wire, you want to SPLICE onto this wire not cut it, this wire sends 12v from ignition switch to Clutch/neutral switch and then to starter relay when key is turned to START.
On an automotive relay(they use standard pin numbering and 30amps) you will hook this spliced wire to Pin 87.
On the ignition switch there will also be a Red/light green wire, this has 12v only when key is on(RUN), again you will SPLICE into this wire and split it into two wires.
These two wires will hook to pin 30 and pin 85 on relay.
Pin 86 will be for your button which will be a ground, so connect pin 86 to one contact on the button and the other contact on the button to a ground.
Pin 87a, if there is one, will not be used.
Yes you could just run the spliced Pink wire to a button and the spliced Red/light green wire to the other contact on the button.
Up to you.
Either wiring setup keeps the Clutch switch or Neutral safety switch working,
And button only works with Key On
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