(a) Not later than August 31 of each year, by majority vote:
(1) the city council of the City of Palestine shall appoint as a voting director one person proposed by the mayor of Palestine; and
(2) the city council of the City of Rusk shall appoint as a voting director one person proposed by the mayor of Rusk.
(b) Not later than September 30 of every third year, by majority vote, the directors appointed under Subsection (a) shall appoint a seventh director.