Hi AlphaWolf,
Please don't let people tell you the bird cannot be tamed. Unless they have extensive experience with taming Ringnecks and also know yours very well, I think you should just consider that they don't know enough about it to make such an assertion. When people tell me I cannot do something I sometimes say "Perhaps you cannot do this, but what I can do has yet to be known." You may say something like that if you like.
A week is a very short time to a Ringneck. He lives in the moment of right now. He has no plans or expectations for the future with you, and so no need to rush. You can take a little hint from him and enjoy what you have even as you consider how he may develop. If you have more of your attention on right now, keeping the future on the side of your mind, you will be able to see more of what happens. Have a plan for the future but enjoy today.
I believe the action you describe of pacing on the perch and warily grabbing a bite to eat while you watch is understandable in a bird who so recently was not even that comfortable with you. He is not comfortable letting down his guard to eat leisurely with you near and watching. Try backing up a few feet or watching from across the room or the doorway.
Give him time and celebrate his small accomplishments. Every long journey is made of small steps. A year from now you can be telling us "Look at everything Aero learned in his first year with me!" People here have heard it from me - Today Rocky learned to follow a food lure. Today Rocky pulled up a toy on a string. Today Rocky learned to fly. Today Rocky chewed up wood for the first time. Today Rocky stepped onto my wrist. Today Rocky ate vegetables. Today Rocky flew to my shoulder. Today Rocky came when I called. Today Rocky went to a stranger. He may not do something new every day, or even every week, but when I sit back to watch and critically evaluate, I usually see something new I missed because I was too busy looking with my heart. It's not bad.

What will Rocky do next? I think he is learning to fly away from the Budgie cage when I point. Time will tell if I'm right.