SECTION 3.04  Organization of Council.
   On or before the fifth day of January next, following each regular municipal election, the members of Council shall meet at the council chambers for the purpose of organization.  At such meeting, the Council shall elect one (1) of its members thereof, other than the Mayor as Deputy Mayor of the Council to serve until his successor shall have been elected.  In the event the Deputy Mayor of the Council ceases to be a member thereof or succeeds to the office of Mayor, the Council shall elect another member, other than the Mayor, to serve as Deputy Mayor until another Deputy Mayor of Council is elected in the manner hereinbefore provided.