In the case of a district where the initial board of directors is to be appointed, the county board of supervisors or the city council that appoints the board of directors shall specify either of the following:
(a) The persons appointed to the board of directors shall serve fixed terms. The directors appointed to the initial board of directors shall classify themselves by lot into two classes, as nearly equal in number as possible, and the terms of office of the class having the greater number shall be four years and the terms of office of the class having the lesser number shall be two years.
(b) The persons appointed to the board of directors shall serve at the pleasure of the county board of supervisors or the city council which made the appointments.