The elective officers of a local hospital district shall be a board of hospital directors consisting of five members, each of whom shall be a registered voter residing in the district and whose term shall be four years, with the exception of the first board. The first board of directors shall be appointed, upon the formation of the district, by the board of supervisors of the county in which the land or a greater part of the land in the district is situated. Upon appointment, the first board shall, by lot, designate two members who shall leave office when their successors take office pursuant to Section 10554 of the Elections Code, and three members who shall leave office two years thereafter. Any vacancy upon the board shall be filled by the methods prescribed in Section 1780 of the Government Code.