(a) The county mayor shall be:
(1) A qualified voter of the county;
(2) At least twenty-five (25) years of age; and
(3) A resident of the county for one (1) full year prior to the date of filing a nominating petition for election to such office.
(b) The county mayor shall continue to reside in the county during the county mayor's term of office, and shall not, during the county mayor's term of office, hold any other public office for profit.