I am not sure what the title of this tune references. My first guess was that Shorty wanted to bank on writing the theme music for the NCAA Big 12 Conference. But it appears that the Big 12 does not extend into Louisiana, so I do not see any sort of connection. Regardless, "Big 12" is an interesting gumbo of afro-cuban and rock rhythms, suitable for any division of competitive activities.
This solo has a very distinct latin flavor. The triplet phrases in bars 3-5 of the solo not only contrast the rigid opening scale, but also paint a picture of the Caribbean. The relaxed feel and use of the blues scale invokes the qualities of a Vin Gordon dub style of trombone playing. The last half of the solo imitates the montuno style of syncopated rhythm often found in Cuban music. So I suggest fetching a bottle of rum for this one.
Oh, wait. Now that look at Trombone Shorty's solo on this tune, I realize that it is only 12 bars long, in what appears to be a 16 bar form. Maybe this solo was a fluke in the recording studio and they named it out of irony. Eh?
No. After doing some light research for a video, it appears that "Big 12" is referring to Trombone Shorty's brother, trumpet player James "12" Andrews. Here's a YouTube video of the two of them closing out the show at the NOLA HOB.
Recommended Reading: Cosmos by Carl Sagan. Published by Ballantine Books.