(a) All persons formerly holding the position of auxiliary police officer in the Police Department shall be eligible for appointment to the hereby established position of part-time police officer in the Police Department, upon their application for such appointment and approval by the Mayor, subject to the satisfaction of such qualifications as the Mayor and Council may ordain.
(b) Any other person satisfying the qualifications for appointment to the position of part-time police officer may apply for such appointment, subject to the approval of the Mayor.