None of y'all don't see Abbott going for a 3rd term in 2022 ?
Even though we don't have term limits, the custom has always been no more than two terms (or no more than 6-8 years back when we had two-year terms). Rick Perry parted with this custom, but that's only because his broke @$$ has never had a real career or any money of his own and he wants to mooch off the fringe benefits of this job for as long as possible. Greg Abbott could never work another day of his life and be just fine, so that's not an issue for him.
The custom was for an incumbent to be defeated in their attempt for re-election.
*** Indicates governors who completed two or more terms and then left office. This last happened in 1968. A first-time voter in 1968, would be 67-years old now.
George Bush (became President midway through his second term).
Ann Richards lost to Bush after 1 term.
Bill Clements did not seek a 3rd term, but had become enmeshed in the SMU scandal.
Mark White lost to Clements after 1 term.
Bill Clements lost to White after 1 term.
Dolph Briscoe lost to John Hill in primary after two terms (one of 2 years and one of 4 years)
Preston Smith finished 4th in the primary behind Briscoe, Cissy Ferenthold, and Ben Barnes
***John Connally served 3 terms (6 years).
Price Daniel lost to Connally in primary after 3 terms (6 years)
***Allan Shivers served 4 terms (the 1st after succeeding as governor).
Beauford Jester died early in his second term.
***Coke Stevenson served 3 terms (5 years). He became Governor when Pappy O'Daniel became US Senator.
Pappy O'Daniel won a special election to become US Senator during his second term.
***James Allred served two terms, and then was appointed a US District Judge.
MA Ferguson completed one term (her second).
Ross Sterling was defeated by Ferguson after one term.
***Dan Moody served two terms.
MA Ferguson was defeated in the primary after one tern.