Sec. 8. If a person appointed as a trustee:
(1) fails to qualify within ten (10) days after notice of the appointment is mailed to that person; or
(2) qualifies but then dies, resigns, vacates the office because that person is no longer a resident of the county, or is removed from office under section 18 of this chapter;
a new trustee shall be appointed by the same appointing authority for the remainder of the vacated term.