ShiroKuro The idea of eye orienting to the thumbs makes a lot of sense to me, because if you know where your thumbs are, you can get the rest of your fingers where they need to be.
It may seem like a good idea, but it isn't. It isn't, because piano music isn't generally built from the thumbs outwards. The most important things are usually found at the top and the bottom. Here are the essential elements, in order of importance:
1. The melody
In most of the music we play, the melody is the most important thing. You will recognise a piece if you hear just the melody. There are times when I've saved my skin in opera rehearsals when the going gets really tough by playing only the melody. It's more important to get the tune (notes and rhythms) right than all the rest. Usually the melody is at the top, but you need to be able to recognise the rarer cases where the melody is in the middle, or at the bottom.
2. The bass line
In classical or romantic music, if you get melody and bass line right, you can already give a good impression of the piece. Most of the time the melody together with the bass line is enough to indicate the harmonies.
3. Other stuff
- harmonies
- accompaniment rhythms
- dynamics
- inner voices
- ornaments
- rubato
- other details...
These elements vary in importance. Probably harmony is the next one to concentrate on, but sometimes a subito ff or pp will trump the harmony. An advanced sight-reader quickly works out what is most important, but if you're a beginner sight-reader it's enough to concentrate on getting top and bottom right.
One more thing: the idea that you must read ahead. If you think you should always be looking at a place further on in the piece than what you are playing, it won't work. What you do need to do is to learn to grasp things phrase-wise, not note by note. I'll post in more detail about how to achieve this when I have the time.