(a) Each director is appointed for a term of office of two years.
(b) The term of office of the first board begins on the date the authority is created. The county judge shall appoint successor directors with the advice and consent of, and from among persons recommended by, all the municipalities within the authority that contract with the authority under this chapter.
(c) If a vacancy occurs on the board or in any office on the board, the board shall appoint a person to fill the vacancy for the unexpired term. However, if the number of directors at any time is less than a majority of the positions on the board because of the failure or refusal of one or more directors to qualify to serve, the death or incapacitation of one or more directors, or any other reason, on the petition of a resident of the authority the county judge shall appoint persons to fill the vacancies.