The City Clerk, while holding such office, and two qualified electors appointed by Council, one from each of the two political parties whose candidates for Governor received the largest and second largest number of votes at the last preceding general election of the State, shall constitute the Election Board of the City. Each Council shall make its appointments to the Election Board within a year after the members thereof take office, and the Election Board so appointed shall hold office until their respective successors are duly appointed and qualified.