Resignations of elected officers and of the City Manager, Clerk, Treasurer, Assessor, City Attorney, and Health Officer shall be made in writing and filed with the Clerk; in the case of the Clerk, such resignation shall be filed with the Mayor; and shall be acted upon by the Council at its next regular meeting following receipt thereof by the Clerk or Mayor, as the case may be. Resignations of appointive officers, other than those appointed by the Council, shall be made in writing to the City Manager, and shall be immediately acted upon by him.