The Governor and Lieutenant Governor shall be elected at the times and places of choosing members of the Assembly. The persons respectively having the highest number of votes for Governor and Lieutenant Governor shall be elected, but in case two or more shall have an equal and the highest number of votes for Governor, or for Lieutenant Governor, the two houses of the Legislature at its next annual session shall forthwith, by joint ballot, choose one of the said persons so having an equal and the highest number of votes for Governor or Lieutenant Governor.