(a) The representatives of the city on the board of supervisors shall be appointed by the council for a term expiring the first day of April in even numbered years and may be removed at the will of the council. Such representatives shall meet all requirements of Chapter 5 at the time of their appointment and may hold other elective or appointive city office or employment. In case any representative of the city on the board of supervisors shall be unable to perform the duties of the office for any reason, the council may appoint another qualified person to serve in his stead.
(b) In making appointments to the board of supervisors, other than appointments to serve during the absence or disability of a city representative, no candidates shall be proposed until one week after the council shall have determined that an appointment is to be made to such office, and the names of all candidates shall be presented at least one week prior to the appointment.