The only other thing would be the condenser (capacitor) and the coil. It doesn't hurt to replace the condenser just as a preventative measure -- they do last a long time. Also, the coil can fail, but that is also a rare occurrence. Be sure, if you are checking the spark, that the coil secondary has a path to ground. If not, the high voltage, secondary winding, output voltage can get very high and short windings in the coil secondary.
This ignition system design is just like the cars had in the 70's and is way over design for a little 12 Hp Kohler engine.