Would you use "Johnny one note" for somebody who is tone deaf? I think it's the title of a show tune from a musical. And I would sometimes hear it used twenty years or so back, but I hardly ever hear it these days. Would you use it?
No, I wouldn't use it. The only thing "Johnny One Note" conjures up for me is the show tune. And to use it about a tone-deaf person would seem pretty unkind, I think - I'd prefer to say "she's tone-deaf".
Beyond show business, the term Johnny One Note is applied as a mild insult to someone who harps on a single theme, or who appears able to do things only one way, or has a very narrow range of skills or interests. I would definitely not use it to describe a tone-deaf person, as it would then become a strong insult.