I've read stuff showing when the different "courses" of priests ministered and the timing was that Elizabeth probably got pregnant right afterward, then 6 months later Mary was impregnated by the Holy Spirit, and that would put the birth of Jesus around the time of the Feast of Tabernacles. This could be appropriate since His death coincided with Passover (
1 Corinthians 5:7), His burial with unleavened bread, his resurrection with First Fruits (
1 Corinthians 15:23), and His pouring out the Promise of the Father with Pentecost or Harvest. Some who teach this also believe that His second coming will be at Trumpets (the trump of God in
1 Thessalonians 4:13-18 and
Revelation 4:1)