(a) The members of the commission shall be appointed as follows:
(1) one member by the commissioners court;
(2) one member by the governing body of the municipality; and
(3) one member by the commissioners court and the governing body of the municipality, acting jointly.
(b) On expiration of a member's term of office, the office shall be filled by the authority that originally appointed the member.
(c) If a vacancy occurs during the term, it shall be filled for the remainder of the term by the original appointing authority.