Look what I've found in the TX Archive videos:
Tuesday, January 15th, 1963
Inauguration of John Bowden Connally, Jr., (D) as TX's 39th Governor at the TX State Capitol South Grounds in Austin: Inauguration of John Connally as Governor (1963)
Tuesday, January 15th, 1991: Dorothy Ann Willis Richards (D) inaugurated as TX's 45th Governor at the TX State Capitol South Grounds in downtown Austin.
*1:42: Bob Bullock (D)'s inaugural address as TX's 38th Lieutenant Governor: he was the last Conservative Dem to hold the Lone Star State's 2nd highest powerful office.