I went back and checked, and the Tampa bowl, fka Outback, has almost never taken a 7-5 team, in fact, maybe never has taken one, we just didn't win enough games.
To have any chance at all at that game, we needed LSU to beat A&M and Ole Miss to beat Miss State, then LSU would maybe have been in a NY6 game and Ole Miss would have taken the Citrus and maybe Tampa would have picked us as the best 7-5 available. But it didn't happen . . . . if we had held on vs. Vanderbilt, I think Miss State and UK would have traded places bowl wise.