Should a vacancy occur on the Council, those Central Committee members living in the City from the same political party of the vacated member shall name a person to fill that vacancy for the unexpired term. If the Councilmember being replaced was not endorsed by any political party, then that vacancy in Council shall be filled by a majority vote of the remaining members of Council. If such vacancy is not filled within thirty (30) days after it occurs, then the Mayor shall fill it by appointment made by a written document filed with the Clerk of Council. The qualifications as provided in Sec. 3.02 of this Charter shall apply.