The City Controller, City Attorney, Treasurer, City Clerk and Director of the Office of Administrative and Research Services shall each designate an assistant or deputy, who shall become the acting incumbent in case of any vacancy in the office. The designation of acting incumbent shall be made in writing filed with the City Clerk, and may be changed from time to time. Upon a vacancy, the acting incumbent shall serve until the office is filled in accordance with Sections 409, 508(b) or 508(c). Any person so designated must possess the qualifications prescribed for the office and shall take the oath prescribed by the Charter before assuming his or her duties as acting incumbent. If a vacancy in the office occurs, and no acting incumbent has been designated, or if the designated acting incumbent is unable to serve, the Council may designate the acting incumbent for the office.