Jim - I have found on these old Kohler K's that have a magneto type ignition, it is very critical that you have the timing right on them (use a timing light if possible). You need to get your hands on a copy of the TP-2379 repair manual or download one from the Kohler site and study the ignition section 8, especially as it pertains to magneto ignition. I would also start by installing a new set of points.
I believe the two wires that go to the welder from the axillary coil are in no way connected electrically to the magneto system. The reason the timing is so important is that the e-gap of the flywheel magnet and coil lamination is determined by this and thus the spark output. Good luck to you on this - Bruce