Hi John,
This is not to difficult,
Now i have the Onan 2.0AJ/R52 Generator but the choke will be the same as yours an is the round shape at your carburetor:

The working of this is as follows:
https://www.youtube.com/shorts/tyhSfzYiPj0So there is only one wire to your choke. This is your positive. Press your starter button. As the "starter" runs (it actually is the generator working as a starter powered by the battery) there should be power at the wire which you can check with a multimeter.
When there is power there, you have the same problem as in the video. Buy a new one.
warning in advance.
A generator can be very dangerous as it is a machine that generates power. When you connect wires the wrong way you can do serious damage or cause fire
so you do this at your own risk! If you are not familiar working with electricity, better get somebody who is!.
Now if there is no power at the wire, you should check why this is. Is the wire loose or is there something wrong with the batterycharger in the wirebox, because that is where the choke gets it's power from via the starter solonoid. Just follow the wire from the choke to where it gets its power from.
Again parts are generally the same so I guess it would be the same with your generator and then the battery charger will look like this:

Here it's the same, when there is no power at the output it needs to be replaced.
Parts are still available.