Don't know if your ignition switch has the terminals letterd but the engine side of the harness goes like this,
Red goes to B switch terminal with 30 amp fuse inline between switch and battery and is connected to POS on battery or POS on starter
White is engine kill goes to M terminal kills engine when continuity to ground
Blue is starter trip wire goes to S terminal goes to flag terminal on starter
Purple is charging or B+ lead goes from center terminal of regulator/rectifier to R terminal on switch and to POS on starter.
Yellow is switched accessory may not be used
Make sure you have an ignition switch that has a M terminal and not an I terminal
If I remember right, the Kohler part # for the ignition switch was 25-099-04? I recommend getting a new switch with an M terminal.