Notwithstanding other sections of this chapter, the City Manager shall not be removed from office during or within a period of 60 days next preceding any general municipal election held in the City, at which election a member of the City Council is elected, nor shall the City Manager be removed from office during or within a period of 60 days next succeeding any general election held in the City at which election a member of the City Council is elected. The purpose of this provision is to allow newly elected members of the City Council to observe the actions and abilities of the City Manager in the performance of the powers and duties of his office. After the expiration of said 120-day period, the provisions of SMC 2.12.260 as to the removal of said City Manager shall apply and be effective.