In my growing up years it was Bama, Auburn, Kentucky & Vandy.
UT's 1st SEC game was always Auburn when I was growing up. In 1988, UT opened with UGA which broke that streak, I think.
Beginning in 1990, with Spurrier's success at Duke (who beat UT) returning to UF that became a big game instantly. Who knew in 1990 that UT and UF would play every year? Prior to the split divisions, UT didn't play UGA or UF very often. UT played:
Auburn
Bama
Ole Miss
UK
Vandy
Rotating opponent: UF, UGA, Miss St., LSU