Each candidate who shall seek a nomination for Governor, under any method provided by law for such nomination, including primary elections, shall at the time of filing for said office designate a candidate for Lieutenant Governor, and the names of the said candidate for Governor and Lieutenant Governor shall be listed on the primary election ballot, or otherwise considered for nomination jointly with each other. No candidate for Governor may designate a candidate for Lieutenant Governor to contest for the said offices jointly with him without the consent of the said candidate for Lieutenant Governor, and no candidate for Lieutenant Governor may designate a candidate for Governor, to contest jointly for said offices with him without the consent of the said candidate for Governor, said consent to be in writing on a form provided for such purpose and filed at the time the said candidates shall file their certificates of candidacy, or other documents by which they seek nomination. In any election, including a primary election, candidates for Governor and Lieutenant Governor shall be listed jointly on the ballot, and a vote cast for the candidate for Governor shall also be cast for Lieutenant Governor jointly listed on the ballot with him, and the election of Governor, or the nomination of a candidate for Governor, also shall constitute the election for the same term, or the nomination, of the Lieutenant Governor who was listed on the ballot or was being considered jointly with him.