Going off a problem I had over 3 years ago, so I can't remember if mine "clicked" or just did nothing, so this may not apply, but a very inexpensive and easy thing to check.
There are 2 switches on the top left corner of my Onan generator, and without looking up the proper names, I think they are a "run" switch and a "Stop" switch. Check the position of those switches. After a bit of searching for the problem, and having talked to many people including an Onan repair company, the simple answer turned out to be correct. I probably accidentally bumped the switches to the wrong positions when I reached across the panel to open the exhaust thru hull.
I didn't find the labelling of these switches to be "self evident", so I added labels to make it clear for me.