I don’t think that you should be spending a lot of time trying to troubleshoot. The cost of the sending unit is anywhere between 28.00-$51.00. I would replace both and and if you are still getting a wrong indication, then move to the instrument.
Based on my experience. just call Kohler directly and have them come and service it before you try to start it for the first time. Most generators don’t get enough use and they suffer from similar issues. Don’t bother waiting for a marine mechanic...