In the event of a vacancy or vacancies from any cause in the office of Mayor or Councilmember, the vacancy or vacancies may be filled as follows:
a. If no more than one (1) vacancy on the City Council exists, a majority of the remaining members of the City Council may fill the vacancy by appointment and the appointee will serve until the next regular City election.
b. If two (2) or more vacancies on the City Council exist at the same time, a special election shall be called to fill the vacancies.
c. Any special election to fill vacancies shall be ordered, held, and conducted in accordance with the general laws of the State of Texas.
d. In the event of a vacancy in any appointive office in the city, new appointments shall be made by a majority of City Council votes on nominations by the Mayor or any member of City Council.