The presiding judge of the early-voting ballot board shall convene the board to count late early-voted ballots cast from outside the country and placed in delivery by 7:00 p.m. on election day, at any time after the last mail delivery occurring two days after the election, or when the early voting clerk certifies that all early-voting ballots mailed from outside the United States have been received, whichever is earlier. The precise time for the convening of the board shall be within the discretion of the presiding judge, with a view toward allowing ample time for the board and the central counting station personnel (if applicable) to discharge its duties so that the county executive committee can timely convene at no later than 1:00 p.m. on the third day after election day.