(1) The terms of members of the board appointed pursuant to subdivisions (1)(e) and (f) of section 46-1217 shall be extended by one year to five-year terms, and the successors to members appointed pursuant to subdivisions (1)(a) through (f) of such section shall be appointed for five-year terms. No appointed member shall be appointed to serve more than two consecutive full five-year terms.

(2) Each appointed member shall hold office until the expiration of his or her term or until a successor has been appointed and qualified. Any vacancy occurring in the appointed board membership, other than by expiration of a term, shall be filled within sixty days by the Governor by appointment from the appropriate category for the unexpired term.