Thanks for the suggestions, Don.
The valves are not tight. I adjusted them a few months ago, and checked them again when this problem cropped up.
Today, I checked the pickup and exciter coils again, this time with a warm engine. The pickup coil resistance was a little higher hot than cold, but still well within the range specified in the factory service manual. The exciter coil was the same hot or cold. The manual does not specify different ranges for hot vs cold.
Still, I have to think that the issue must be with the exciter or pickup coil, since I can't see how it could be anything else.
I'll be looking for a good used stator and pickup coil on ebay.
Frank