If, in any matter pending before the Council, a council member is disqualified to act for a reason that would disqualify a judicial officer from sitting in a matter, the Council may proceed to consider the matter, if a quorum is present, or may certify to the officer having the appointment of that member, who shall thereupon immediately appoint a special member to sit in that case, only. If the appointing officer makes no appointment within ten (10) days after the mailing of the certification of disqualification to the appointing officer, the Council shall appoint a special member.