The generator starts up runs for about 15 seconds and shuts down.

Turns out it was the Manual-off-Auto switch that was bad. My DVM showed a voltage drop across the switch. The controller wasn't getting enough power.

One good thing about it was it forced me to really study the schematics to understand how everything worked. I'm now in the process of designing my own esp32 based controller, with wifi connectivity, to replace the stock control board.

low voltage can be from incorrect running rpms
as it is new out of the box I suggest that you get a service under warranty to sort out any problems

You need to determine if it is a Brushed or Brushless generator and follow the tests on the link below. (You will locate the brushes on the end of the alternator in a 12o'clock position if they are fitted).

http://www.generatorguru.com/help-me-fix-my-generator-repair-advice/

Then contact Generator Guru with the results and they will let you know what needs replacing. This is a free service.
http://www.generatorguru.com/help-me-fix-my-generator-repair-advice

There are several Generac forums available:

generac forum Bing

Check the ATS shutdown cirucuit connections.

I would do a compression test before you removed a cam.
How did you diagnose the camshaft?

Good troubleshooting on your part. Was my thoughts that the onboard battery had failed.

John did you ever get this problem solved because I too am having a similar problem however for me it is also not shutting down automatically when the power is restored

You can check for tanks being turned off and of course if there is fuel in the tanks. If further troublshooting is necessary you should likely ask for assistance.

Did you remember to set the overspeed shutdown threshold on the control board?