So sorry Libby, but I'm afraid that if anyone were to e-mail the person who has the ringneck, it could only make the situation worse, not better.
I wish the person who has the ringneck would at least allow you to look at him and see if it is Rhemey, although I'm not entirely sure how DNA testing would help unless they have a way to show relationship. I just haven't heard of a test within birds that does that, although I could be wrong.
I have a cockatiel that was found by the previous (not sure people is the appropriate word, for how they cared for their animals... perhaps monsters? ignorant of their animals health issues and never once took them to a vet) and never once did they consider looking for the previous owner. She was found in their yard and supposedly they got her into better health.... however, she was fed crappy Walmart seed, stuck in a "finch" cage (big enough for her to stand in, but not necessarily big enough to spread her wings - barely any room between cage bottom and cage top when she was directly in the middle), and expected to learn to talk and smoke pot. When their expectations of what she was supposed to be like fell through, she got ignored. They "simply forgot" to clean her cage, "simply forgot" to feed her, and "simply forgot" to make sure she had fresh water. She also became a chronic egg layer in a smoke filled home (ceilings stained yellow - smoke moved around the room when you walked through), kept in a dark room (blanket over the window) and kept covered 24/7 because she was "too noisy".
When I took her in, she was near 50% underweight and so weak that you could easily catch her in the air if she flew, and she did not land with grace. I did try to search for her owners, but she had been missing for around a year by then. Eight years later and she's doing well! At a great weight and eats healthy!
So I can kind of understand the frustration of someone not willing to do the right thing and search for the rightful owners. If it was a dog or a cat, it would *usually* be no issue to find it's home, but a bird? Many people think to keep instead of looking for the owner.