Amadou Mahtar M'Bow's bid for an unprecedented third term as head of UNESCO fell short again in the third round of voting by the executive board. M'Bow, of Senegal, who has been director general of the Paris-based organization for 13 years, received 23 of the needed 26 votes from the 50-member executive board, officials said. Former Spanish Education Minister Federico Mayor finished second with 18 votes. Board members of the U.N. Educational, Scientific and Cultural Organization planned a fourth secret ballot tonight. If there is still no winner, a runoff between the two leading candidates will be held. Opposition to M'Bow's policies led the United States to withdraw from UNESCO in 1984.