FWIW, the Governor of Texas doesn't actually do anything.
Not true! He can...um...uh...he can...he can call the state legislature into special session! Repeatedly!
(That really is the main function of the Governor of Texas, but one utilized quite often in a state where the legislature is only scheduled to meet for one 5 month session once every two years.
Interesting to know. It would be interesting if a libertarian were elected Governor of Texas & then the legislature was never called into special session.