In a city, one of the four members of a housing authority appointed by the mayor shall be a resident of that city and shall be a representative of organized labor who shall be appointed by the mayor from a list of not less than two nor more than five names, representing different unions submitted by the Central Labor Council, AFL–CIO and the International Brotherhood of Teamsters, Chauffeurs, Warehousemen and Helpers of America of the city or of the district within which the city is included. If no such list of names is submitted within sixty days after a vacancy occurs, the mayor may appoint any representative of organized labor of his own choosing to the authority. In a city, one of the four members of a housing authority appointed by the mayor shall be a tenant in a building owned and operated by or on behalf of the local housing authority who shall be appointed by the mayor from lists of names submitted by each duly recognized city-wide and project-wide tenants' organization in the city. A tenants' organization may submit a list which contains not less than two nor more than five names to the mayor who shall make his selection from among the names so submitted; provided that, where no public housing units are owned and operated by the local housing authority and no such units are owned and operated on behalf of the local housing authority, the mayor shall appoint any tenant of the housing authority from lists submitted in accordance with this section. If no list of names is submitted within sixty days after a vacancy occurs, the mayor shall appoint any tenant of his choosing to the authority. The mayor shall notify in writing tenant organizations as specified herein not less than ninety days prior to the expiration of the term of a tenant member. Whenever a vacancy