A vacancy in the office of a member of the metropolitan council shall be filled in the same manner as provided for the original selection. The meeting of mayors to fill a vacancy of the member selected under the provisions of RCW 35.58.120 or of special district representatives to fill a vacancy of a member selected under RCW 35.58.120 shall be held at such time and place as shall be designated by the chair of the metropolitan council after ten days' written notice mailed to the mayors of each of the cities specified in RCW 35.58.120 or to the representatives of the special purpose districts specified in RCW 35.58.120, whichever is applicable.