Following some questions, we’ve changed the language in the Constitution to reflect the idea that:
A player is eligible at all positions he played 15 or more games at in the major leagues. If the only position he played 15 or more games was DH, he’s DH/Util eligible only for the draft.
If a player didn’t appear at any major league position at least 15 or more times, he’s then eligible at the single position other than DH he played most at all levels he played the year before combined, unless he didn’t play 15 or more games at any other fielding position. In which case he’ll be DH/Util eligible only for the draft.