Any person intending to contest the election of any one declared by the Governor to have been chosen an elector of President and Vice President of the United States, shall, within 10 days after such declaration by proclamation of the Governor, give written notice of such intention to the person whose election the contesting person intends to contest and also to the Governor, and within 5 days after the delivery of such notice, shall deliver to the person whose election the contesting person contests and to the Governor written specification of the grounds upon which the contesting person intends to contest the election of the person so declared to have been elected. If 1 of the grounds shall be that illegal votes were given at such election for the person declared to have been elected then such specification shall particularly set forth the name of each alleged illegal voter, with the several objections to the legality of that voter's vote, and shall also distinctly set forth and state the election district at which the alleged illegal vote was cast.