The board of supervisors of the office county shall fill by appointment vacancies in the offices of directors, provided that any such appointed directors shall be required to run for election in the next succeeding general district election.
If within 60 days after a vacancy on the board of directors occurs the board of supervisors has failed to fill such vacancy, a special election may be called by the board of directors and held in the division affected, for the purpose of filling such vacancy. In the event there are more than two candidates at such special election, only a plurality will be required for election. The candidate elected at such special election shall fill the unexpired term of the vacating director.