The Middle Distance

That's a very sensible explanation, and I think I'm coming around to the "no" way of thinking, or at least the "probably not, BUT..." side. I think it's also worth considering that treatment of the Ring itself isn't consistent at all between The Hobbit and LOTR, so there's another dimension of wiggle room there.

However, if maybe the POSSESSION seems obvious and matter in fact(required for certain dynamics perhaps), only then would I argue for disappearing cock.

Oh, now this is interesting! Bit of a D/s dynamic, perhaps? Does it make a difference if the Ring-wearer is aware of what it is and what it really does, and is using that power? (as opposed to: cool! magic ring! makes me invisible!)