In accordance with Section 7 of Article V of the Illinois Constitution of 1970, if the Attorney General, Secretary of State, Comptroller, or Treasurer fails to qualify, or if his or her office becomes vacant, the Governor shall fill the office by appointment. If there are 28 months or less remaining in the term at the time of the vacancy or failure to qualify, the appointed officer shall serve for the remainder of the term. If there are more than 28 months remaining in the term at the time of the vacancy or failure to qualify, the office shall be filled by a special election to be held at the next general election. In the case of a special election pursuant to this Section, the appointed officer shall serve until the election results are certified and the person elected at the special election is qualified. Nominations shall be made in accordance with Section 7-68 of this Code. For purposes of this Section, a special election shall not be held if the person elected to the office failed to qualify for a period of less than 30 calendar days. The office to be filled by special election shall appear on the regular ballot at the general election, and shall not require the use of a separate ballot.