A vacancy in the Council, whether it be in the office of Mayor or Council Member, shall be deemed to exist if the incumbent Council Member or incumbent Mayor is no longer a resident of the City, dies, resigns, is removed from office, is convicted of any felony or any offense involving violation of the official oath, fails to take and file the oath of office, at or before the date of the second regular meeting of the Council held after January 1 next following the election at which elected or the second regular Council meeting held after the appointment is communicated to an appointee, or continuous absence from the City in excess of three months. In each such case, the Council shall by resolution declare such vacancy to exist and shall forthwith appoint an eligible person to fill the same until the next regular municipal election, when the office shall be filled for the unexpired term. No change in Ward boundaries shall in any way affect the then current term of any Council Member.