If a vacancy occurs during an odd-numbered year or after the 62nd day before general primary election day in an even-numbered year, the remainder of the unexpired term shall be filled by a special election in the same manner as provided by Chapter 203 for the legislature, except that:
(1) the minimum number of signatures that must appear on a petition accompanying a candidate's application for a place on the ballot is 5,000; and
(2) Section 203.013 does not apply.