I had a similar situation and found the following. The rocker switch at the generator was full of dust and dirt and was not returning to the neutral position when it was used to either start or stop the generator. It was hardly noticeable that it was not properly at rest.
After seeing the difference and cleaning the switch with some electrical contact cleaner and allowing it to go to its true rest position everything worked as advertised. As you might have guessed the inoperable switch prevented the interior switch from doing its job.
Check it out.
jwmII