In those counties in which the election of members of county boards of education are required to be held on the same date as prescribed for the election of members of governing boards of school districts, as provided in Section 1007, the offices of those members of the county board of education whose terms have been fixed to expire in even-numbered years shall become vacant upon the expiration of those terms. The vacancies arising shall be filled by the majority of the remaining members of the board, and the appointees shall hold office only until the first day of July following the election of their successors.