What is SAM is that the ignition part that is impossible to find?
Yes. That is the Spark Advance Module. One thing to check with the SAM. If you can loosen it enough, turn it over and inspect the epoxy potting material on the back for any signs of cracks. If that material cracks, it lets in moisture and that would likely cause it to no longer work properly.
There is a conversion kit that would eliminate the SAM. It comes with two new ignition modules and a new flywheel. The timing is different so the modules you just bought would become useless to you. The kit part number is 24 755 308-S. It has a suggested list price of 220.00. I know it doesn't look like it but it's actually a good deal. If you were to buy just the flywheel it has a list price of 272.00.
If it comes down to it you might be able to find a used or new old stock SAM. You would be looking for a part number 24 584 09-S or a 24 584 10-S. The two are the same electrically. The only difference is one had spade connectors where the other had bullet connectors.
If you have any good long established Kohler dealers near you they may have a SAM tester. It would be doubtful any Kohler dealer in business for less than 15 years would have one. Your best bet would be an "Expert Dealer". If you go to Kohler's website and search for dealers by zip code "Expert Dealers" are clearly defined.