Here is where things gets complicated. you can get the 24 584 36-s ( 2 wire not 3)modules by themselves for replacement, but the 24 584 31-s SAM is NLA. So if somebody needs just the ignition module then you can get the ignition module but if you need a SAM then you have to order the 25 707 03-s kit. The 25 707 03-s Kit contains 2 new MDI modules, the necessary new kill wire, and a need spade connector to connect to the old kill wire. The old hot wire that went to the SAM gets taped up out of the way and then you remove and throw away the old 24 584 31-s SAM and both of the 24 584 36-s modules.
The different ignition systems are confusing because there was an analog SAM(ASAM) and digital SAM(DSAM) which gets converted to the MDI system. The DSAI system which used 3 wire ignition modules, but no SAM. and now the MDI, which look like normal single wire ignition modules, but you don't have to set an air gap because they are a set position not adjustable ignition module on the newer engines. The conversion kit only is used on the DSAM system.
So when you gave the ignition module part number is doesn't reference the parts bulletin, When you mentioned the SAM part number then that triggered the conversion bulletin. For me when I have an older Kohler with SAM with an ignition problem, I always check the SAM part number against the bulletin to see if it upgrades to the MDI system instead of just replacing the faulty ignition module.