Finally got to work on the Walker late this afternoon. The regulator/rectifier is a finned aluminum device bolted to a bracket (2 bolts) located on the exhaust side of the engine (the opposite side of the engine from the flywheel) half under the cooling fan shroud. I removed the shroud (2 bolts and 3 Phillips head machine screws) to get better access to the regulator/rectifier mounting bolts. I removed and unplugged the device and probed the 2 white wires on the engine side plug with my DMM and started the engine.
At full throttle the voltage across the white wires was 42.2 volts AC, well within the "28 volts or more" spec and the voltage increased/decreased smoothly as I revved the engine. I got this spec from the Kohler Aegis LH 685 engine manual I downloaded for free on the internet. So, phew, the stator is OK. I'll call the local Walker dealer tomorrow to see if they have a regulator/rectifier in stock. I am very sure of my diagnosis but I hope to have them test the regulator/rectifier if they have a tester just to make double sure. :thumbsup:
I'll be back to post the final results.
BTW-after the testing, I reinstalled the cooling fan shroud and mowed my lawn on the battery. It only takes about a half hour and afterwards I put the battery on the charger.