The Council shall select and appoint, on the basis of executive and administrative qualifications with special reference to training and experience, a person to the position of City Manager for an indefinite period, and shall determine the compensation for this officer. The City Manager shall serve at the pleasure of the Council and shall be the chief administrative officer of the City. Any person who has been elected or appointed to the Council shall not be eligible for appointment as City Manager until two years have elapsed following the expiration of the term for which the person was elected.