Within 45 days after the occurrence of a vacancy in an elective office subject to this article, the vacancy may be filled by Town Board appointment. If an appointment is not made within 45 days, the vacancy may be filled by either:
A.
Special election called by the Town Board, to be held not less than 60 days and not more than 90 days from the date the Town Board decides to call for a special election; or in the next general election, whichever will allow the vacancy to be filled in the shortest space of time reasonably possible.
B.
Notwithstanding the foregoing provision, if a vacancy in an elective office cannot be filled by appointment and the time for holding a special election to fill such vacancy occurs within 90 days of a general or other special election, the office shall remain vacant until filled at a special election on the same date as the general election or previously scheduled special election; and no special election to fill an elective office shall be held during the months of July or August. In the event the time for holding a special election to fill a vacancy in an elective office occurs in the month of July or August, then the time for holding such special election shall be extended an additional 60 days.