Probably none of that, since a ring is made for a finger. It probably magically detects if it has made contact with one. Now, if the question was what if it was put on a severed finger, then that is something to think about
So if someone was fingerblasting Frodo with the ring on, and then someone cut their finger off mid fingerblast, you're saying that only the finger would turn invisible, and not Frodo? Even if it's in his butt?