Part of the rule:
"17.10.5.1 Maximum Limitations—Institutional. [FBS/FCS] In bowl subdivision football, a member institution shall limit its total regular-season playing schedule with outside competition during the permissible football playing season in any one year to 12 contests (games or scrimmages), except as provided for member institutions located in Alaska and Hawaii, under Bylaw 17.28.2, and except as provided for all members under Bylaw 17.10.5.2. In championship subdivision football, a member institution shall limit its total regular-season playing schedule with outside competition during the permissible football playing season in any one year to 11 contests (games or scrimmages), except as provided for member institutions located in Alaska and Hawaii, under
Bylaw 17.28.2, and except as provided for all members under Bylaw 17.10.5.2. Twelve football contests shall be permissible during those years in which there are 14 Saturdays from the first permissible playing date through the last playing date in November"

and

"Hawaii, Alaska, Puerto Rico. Any football games played in Hawaii, Alaska, or Puerto Rico, respectively, either against or under the sponsorship of an active member institution located in Hawaii, Alaska or Puerto Rico, by a Division I member institution located outside the areas in question"

So it sounds like if a school plays Hawaii, or plays in a game against another school and the game is sponsored by Hawaii, then you can get the 13th game.

Also, it appears you can play a 13th game if you play in an international game, but only once in a 4 year period.