Christmas: Date revealed by Levite calendar & celebrated through the ages! - American Minute with Bill Federer
John Chrysostom (349-407), Archbishop of Constantinople, accepted that Zachariah was in the Temple the week of the Day of Atonement and Feast of Tabernacles.
Susan K Roll wrote in Toward the Origins of Christmas (1995, pp. 100-101):
"Chrysostom's third argument follows ... that Zachariah was ... priest during the Feast of Tabernacles in the year John the Baptist was conceived.
Chrysostom counts off the months of Elizabeth’s pregnancy, and dates Mary’s conception from the sixth month of Elizabeth’s ... then counts off another nine months to arrive at the birthdate of Christ."