Kendall, Richard P,
Kohler had/used at least 4 (actually 5 I believe)different magneto systems of thier own design on the K161, and the system used on the Cub Cadet Original, 70, 71, and 72 with recoil start was what the Kohler parts manual calls the L1 Stator, Rotor-magneto assembly. The original P/N for the assembly was C-230089, and it uses a rotating magnet, P/N 230360, that slips over the crankshaft and is keyed to it. The flywheel, Kohler P/N 231276, is used on both the electric start and recoil start K161 versions used in the Cub Cadets. There were versions of the K161 that had a stator alternator that used flywheels with built in magnets, but they were not used as original equipment in/on Cub Cadets. You can see a breakdown of the magneto in the parts look-up above, just type in Cub Cadet for the model number since the Original does not have a model number, to see the engine and mag for the Original
Part of the problem I have seen with the coil is the case (or core, for lack of a better words), cracks over time, and the performance of the coil decreases. The coil case/core on my 72 was cracked when I got it, and the condenser had been replaced with a battery ignition type condenser mounted on the outside of the blower housing, and spliced into the wiring going to the points. I don't know if it worked or not, because I replaced both with the correct parts from another recoil start engine.