1.  On entering upon the discharge of the duties of the office of county commissioner, each county commissioner, whether elected or appointed, shall take and subscribe to the oath of office as prescribed by law.

2.  If a county commissioner shall neglect or refuse, during the period of 15 days from and after the first Monday of January succeeding his or her election, to take the oath of office as herein directed, his or her office shall be deemed vacant, and such vacancy shall be filled by appointment.