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657 is the model number. There is only one other and it is a 657A, both use the same engine. The Kawasaki voltage regulator, has three terminals. the two from under the flywheel would have AC output of 28 volts are more, and go on each of the outer terminals, the center terminal is the DC output and would go to the battery positive, at the starter solenoids positive post, or to the battery terminal of the keyswitch.
To find a wiring diagram it would take a service manual, and I don't have one. Push button for starter has to be previous owner! It came with standard keyswitch start.
OK, check the two on the plug for at least 28 volts AC. an check the open terminal for 14 volts DC. I could be wrong, I thought Kawasaki was same wiring on regulator as Kohler.
Did it check out?