Independent or from a Major Football Conference, with a single exception:
BYU on January 1st, 1997--then a member of the WAC.
That distinction has been broken twice under the current NY6/G5 auto-qualifier rules beginning with Western Michigan on January 2nd, 2017.
WikipediaThe Cotton Bowl Classic, also simply known as the Cotton Bowl, is an American college football bowl game that has been held annually in the Dallas–Fort Worth metroplex since January 1, 1937. The game was originally played at its namesake stadium in Dallas before moving to AT&T Stadium in nearby Arlington in 2010. Since 2014, the game has been sponsored by the Goodyear Tire and Rubber Company and officially known as the Goodyear Cotton Bowl Classic. It has been previously sponsored by Southwestern Bell Corporation/SBC Communications/AT&T (1997–2014) and Mobil (1989–1995).
https://en.wikipedia.org/wiki/Cotton_Bowl_Classic