The board members appointed to the metropolitan district shall hold office for three-year terms, except that for members first appointed, such members shall be staggered as evenly as possible between terms of one year, two years and three years. The executives of the counties within the metropolitan district shall meet to determine and implement a fair allocation of the staggered terms among the counties, provided that counties eligible to appoint more than one board member may not appoint board members with identical initial terms until each of a one-year, two-year and three-year initial term has been applied to such county. On the expiration of such initial terms of appointment and on the expiration of any subsequent term, the resulting vacancies shall be filled by the executives of the respective counties, with the advice and consent of the respective governing bodies. All vacancies on the board shall be filled in the same manner for the duration of the term being filled. Board members shall serve until their successors are named and such successors have commenced their terms as board members. Board members shall be eligible for reappointment.