I think you've solved it correctly. Mine works this way too. Another way to phrase it so that it makes sense to everyone is, that while other engines seem to "run along" or "take" on their own once you kick things into motion, the Onan wants me to hold the button until the generator is running all the way (not really holding after it's started, just till it's started, which seems like a longer start phase than other engines). It doesn't want me to release the start button until its started for sure. Other engines seem to run along, like the car engine or the 454 moho engine...you can turn the start key for basically just a blip, and then the engine seems to have a life of it's own in less than second whereas the gen really appreciates a longer start-hold phase.