Any mayor who decides to become a candidate for council shall, unless his term as mayor shall expire in the year of the election, resign his position as mayor not later than sixty (60) days prior to the filing deadline for mayor or council, by tendering his irrevocable, written resignation to the city clerk, such resignation to become effective upon the seating of the next succeeding city council in January. If the resignation is not received by the city clerk at least sixty (60) days prior to the filing deadline for mayor or council, the mayor shall be deemed ineligible to seek the office of council in that election. The vacancy, if any, created by such resignation shall be nominated at the primary and filled at the general election for the balance of the mayor’s term so vacated. No individual shall at the same election be a candidate for both mayor and councilperson.