When a person appointed to succeed to the office of lieutenant governor succeeds to the office of acting governor, the acting governor shall, by proclamation, call a special primary election to be held on a date not less than 60, nor more than 90, days after the date the vacancy in the office of the governor occurred and a subsequent special election to be held on the first Tuesday that is not a state holiday occurring not less than 60 days after the special primary election. However, if the vacancy occurs on a date that is less than 60 days before or is on or after the date of the primary election in years in which a governor is regularly elected, the acting governor shall serve the remainder of the unexpired term and may not call a special election.