The members of each local board first appointed shall be appointed initially for terms of from one to four years so as to provide for the balanced overlapping of the terms of the membership thereon and the members of a local board representing more than one county or city shall be appointed initially for such terms, of not less than one nor more than four years, as may be determined by the governing bodies of their respective counties or cities. Subsequent appointments shall be for a term of four years each, except that appointments to fill vacancies that occur during terms shall be for the remainder of those unexpired terms. Appointments to fill unexpired terms shall not be considered full terms, and such persons shall be eligible to be appointed to two consecutive full terms. No person may serve more than two consecutive full terms; however, this section shall not apply to a member of a local board who is also a member of the board of supervisors for a county represented by the board, who shall serve at the pleasure of the board of supervisors of which he is a member or until such time as he ceases to be a member of the board of supervisors, or in cases in which a local government official is constituted to be the local board. A member of a local board who serves two consecutive full terms shall be ineligible for reappointment to such local board until the end of an intervening two-year period dating from the expiration of the last of the two consecutive terms.