Before entering upon the duties of office, every appointive officer shall take and subscribe to the usual oath of office as provided by the State Constitution for State officers. The oath shall be filed with the Clerk. Failure by an officer to take, subscribe, and file with the Clerk the oath of office within ten (10) days from the date of notice shall be deemed a refusal to serve, and the office shall be deemed vacant unless the Council shall extend the time in which such officer may qualify.