directors who must reside in a division but be elected at large, the number of candidates for director at large from a division does not exceed the number required to be elected director at large while residing in that division; and if a petition signed by 10 percent of the voters or 50 voters, whichever is the smaller number, in the district or division if elected by division, requesting that the general district election be held has not been presented to the officer conducting the election, he or she shall submit a certificate of these facts to the supervising authority and request that the supervising authority, at a regular or special meeting held prior to the Monday before the first Friday in December in which the election is held, appoint to the office or offices the person or persons, if any, who have filed declarations of candidacy. The supervising authority shall make these appointments.

candidacy for any office, the supervising authority shall appoint any person to the office who is qualified on the date when the election would have been held. The person appointed shall qualify and take office and serve exactly as if elected at a general district election for the office.