Any councilperson who decides to become a candidate for mayor shall, unless his term as councilperson shall expire in the year of the election, resign his seat on the city council not later than sixty (60) days prior to the filing deadline for council or mayor 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 councilmember shall be deemed ineligible to seek the office of mayor 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 council term so vacated. No individual shall at the same election be a candidate for both mayor and councilperson.