Final answer:
In Texas, the Governor can appoint a state judge when a vacancy occurs, with these temporary appointments lasting until a special election is conducted.
Step-by-step explanation:
Although judges are elected in Texas, the Governor can appoint a state judge in the event of a vacancy. This process is in accordance with the 17th Amendment, which allows for temporary appointments by the state executive authority until a special election can be held, if the state legislature has authorized such a process. Unlike federal judges appointed by the President, state judges can face elections depending on the state's laws.