When the polls are closed, the precinct board [election board] shall proclaim that fact aloud at the place of election. After the proclamation no voter shall cast a vote. However, if at the hour of closing there are other voters in the polling place, or in line at the door, who are qualified to vote and have not been able to do so since appearing, the polls shall be kept open a sufficient time to enable them to vote. In the instructions to the precinct board [election board] the secretary of state shall specify procedures whereby the precinct board [election board] shall determine the identity of the last person in line at the time the polls closed.