Small Engine Troubleshooting Problems? Ask a Mechanic Now.
See 7.7 in the manual link above.
I wish it was that easy, but I have no schematic for the tractor. But if you have the old engine, look at the three wires that are there, and identify where each wire goes to. Then do the same with the new Kohler. That will leave only wire wire , and identify where it goe to, an let's see what can be done with it!
I see question is still open, did you find the right wires