I personally attribute Connally's cachet with the GOP to his service of Nixon, and if Nixon loses, he kinda loses that. It's why Pompeo '24's gonna be a dud (among other reasons).
Of course, he could switch parties on his own if he still feels isolated from the Democrats. I don't see why he couldn't join the Republicans and run for Governor again after the Sharpstown scandal. He'd probably fare better than Hank Grover did!
