Blueoyster101 provided the answer I needed, with my acceptance of the (bizarre and inexplicable) side effect that turning off synching hides all existing Notes. Happily I didn't have any Notes I wasn't prepared to lose.
jessicafromlower hutt's information was interesting, but since I don't have a Mac, or Mac email (just a 3g iPad), not sure how to apply it. I gather it's Mac email's configuration of the gmail account, not something on gmail.
I'm replying to honolulu75, because I agree the issue is very frustrating, but completely disagree that this is "way too simple." The Notes app designers made a strange choice, and provided no means to modify it. Turn off synching and lose access to saved information? That's crazy.