(a) The board shall, by appointment, fill within forty-five days any vacancy that occurs in its membership. In the event that the board does not fill the vacancy within forty-five days, the state Superintendent of Schools shall appoint a person to fill the vacancy.
(b) (1) When the vacancy occurs after the eighty-fourth day before a general election, and the affected term of office ends on June 30 following the next primary election, the person appointed to fill the vacancy shall continue in office until the completion of the term.
(2) When the vacancy occurs after the eighty-fourth day before a general election and not later than the close of candidate filing for the next succeeding primary election, and the affected term of office does not end on June 30 following the next primary election, an election for the unexpired term shall be held at the next primary election, and the appointment shall continue until June 30 following the primary election with the duly elected and certified successor taking office on July 1, following the primary election and serving until the expiration of the original term of office.
(3) When the vacancy occurs after the close of candidate filing for the primary election and not later than eighty-four days before the general election, the vacancy shall be filled by election in the general election, and the appointment shall continue until a successor is elected and certified.