This article, while written last year, is well done and helps explain things rather well.
http://www.cougcenter.com/wsu-cougars-football/2015/11/16/9748014/pac-12-bowl-selection-process-tie-ins
Here is a pertinent part:
The fudging room disappears, though, for the final three bowls. By Pac-12 rules, these games have to select based on conference finish (though they can have their choice of tied teams), so the Sun Bowl was forced to take ASU (although “forced” is funny because we can presume the folks in El Paso were absolutely tickled to land them), Vegas took Utah and the Cactus took UW.
This is such a complete article that I would think that if there was any sort of “not 3 in a row” rule, it would be brought out here. But there is no mention of it.
It does mention that committees of the specific bowls may not have representatives multiple times because they had them recently, but there’s nothing that speaks of a mandate.
And in my mind, the Vegas Bowl, who ends up picking close to the bottom of the list, would be tickled to have Utah anyway because it’s just down I-15. Better Utah than Colorado or the Central California, Oregon, or Washington Schools. They’d more easily sell the bowl out that way.
Utah @ 
UCF 
.
