(a) If any vacancy occurs in the party nomination of candidates for office nominated at the primary election or by appointment under the provisions of section eleven of this article, the vacancies may be filled, subject to the following requirements and limitations:
(1) Each appointment made under this section shall be made by the executive committee of the political party for the political division in which the vacancy occurs: Provided, That if the executive committee holds a duly called meeting in accordance with 3-1-9 of this code but fails to make an appointment or fails to certify the appointment of the candidate to the proper filing officer within the time required, the chairperson of the executive committee may make the appointment not later than two days following the deadline for the executive committee: Provided however, That for a delegate district or senatorial district situated entirely within a single county, the county executive committee, or its chairperson if the committee fails to act, may fill the vacancy and certify the candidate named to the appropriate filing officer.