Sec. 8. If a person appointed as a trustee:
(1) fails to qualify within ten (10) days after notice of the trustee's appointment is mailed to the trustee; or
(2) qualifies but then dies, resigns, vacates the trustee's office because the trustee 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.