So this is what I come up with when I look your engine up on my distributor's portal: 2458463-S 24 584 89-S ! MODULE, SPARK ADVANCE (DSAI) ASSEMBLY - DISCONTINUED SEE PB 259 You listed part number 24-584-36-S . I suppose that it could be correct, but I would match the number to an old coil.
Kohler had several different ignition systems. On yours your kit comes with both coils and the harness to replace the original smart spark . The SAM coils have extra terminals. I assume that if yours had just the single terminal, it was converted already. I'm not sure that I have the coil numbers from the kit. Price wise it is an affordable kit. I suppose that it is possible that the capacitor releases the spark at the wrong time? You should be able to find Kohler Parts Bulletin 259 on the web for more details.
Kohler 12 volt Digital Spark Advanced Ignition (DSAI) has been discontinued. A new magneto powered spark advance system MDI has taken its place. This new MDI system no longer requires 12 volts to function.
DSAI Ignition System parts and kits will no longer be available. Replacement of current DSAI ignition parts requires an MDI conversion kit. The MDI kits require use of the original engine wire harness.
The following table shows the various DSAI system modules and where they were used. The chart identifies the needed kit to convert to MDI.
After the conversion from DSAI to MDI Ignition, the modules can be replaced individually.
DATE REVISEDDATE ISSUED
MODEL
NO.
ENGINE DIVISION, KOHLER CO., KOHLER, WISCONSIN 53044
Parts Bulletin 259
9/13
Engine Model
Previous Ignition Module MDI Module Conversion Kit CH/CV740 24 584 52-S, 24 584 63-S, 24 584 89-S Ignition Module 25 707 03-S CH/CV740 24 584 31-S Speed Advance Module 25 707 03-S CH/CV750 24 584 53-S, 24 584 64-S, 24 584 90-S Ignition Module 25 707 03-S CH/CV750 24 584 39-S Speed Advance Module 25 707 03-S SV735/740/840 24 584 63-S, 24 584 89-S Ignition Module 32 707 01-S SV735/740/840 24 584 31-S Speed Advance Module 32 707 01