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Kohler model number? The charging coil (stator) is under the flywheel and has two wires that go to the voltage regulator, the tow wires from the coil produce AC volts and reading needs to be 28 volts AC or more, with plug off the regulator. If it has 28 volts or more, it is good. The regulator then is tested, the center post is the output to the battery and would read around 14 volts if it is good.
Here is manual for CV series Kohler. See section 8 for the electrical.