Finding our which is the dominant eye is not theory - it is fact. If you look with both eyes at an object across the street, ie: basketball hoop, and placing your thumb over it, your dominant eye will control the position of your thumb. Closing the left eye for a right eye'd person leaves the object covered, no thumb movement. Closing the right (dominant eye) caused your thumb to jump to the right.
For a left eye'd person, closing the left eye will make the object jump to the left.
When doing this 'test' concentrate on the object beneath your thumb, not your thumb itself. For a person with close eye dominance, concentrating on the thumb, can show cross dominance, ie: I'm right eyed, but if I concentrate on the thumb, I also see a non-thumb-covered basketball hoop to the left of the one covered with my thumb. Moving my thumb over to the one on the left, then closing the right eye, leaves my thumb on the hoop which would indicate I'm left eye dominant - I am not.
You have to concentrate on the object, not your thumb.