Look, read posts 4, 16, 19. Youll see the regulator is not the issue here !
Kohler SAM and DSAI ign systems/modules require apx. 12v to function. They usually get this 12V from the machine wiring, not the engine wiring. If the battery is not supplying 12V for whatever reason, the motor dies.
The regulator FEEDS the battery and the bat. feeds the rest of the system. Again, not all systems work like this, some regulators DO have a sensing circuit that needs 12V into it.
As for yer walkers, they died cause the battery wasn't getting charged due to the poor reg. connection.
Kohler manuals are a free download. If ya don't have any actual experience, then get a manual or two and STUDY.
Any questions, call me in the morning! I'm outtahere.
( almost gametime)