Q: What is the significance of Christ's birth in relation to the Feast of Tabernacles? I've heard that the timing of His birth can be calculated by using Zacharias' term of service in the Temple (house of Abia, I Chron. 24), and Elisabeth being in her sixth month of pregnancy at the time Mary was chosen.
A: If we knew for certain exactly when the course of Abia functioned in the Temple, we could certainly determine very closely the exact time of year that Yeshua was born. Unfortunately, this source of information is in rabbinic writings which are contradictory. Because of the contradictions, we cannot be 100% sure which ones are right, or even if any of those rabbinic traditions are correct. For that reason, scholars who work with the sources must come to the conclusion that the date of the Lord's birth is still indefinite.
Quite a few people in recent times, especially in the messianic movement, but also elsewhere, have desperately been trying to connect the birth of Yeshua with the Feast of Tabernacles and, therefore, will cite one source while ignoring the others, but that is not really fair to the material. I do not think anyone should dogmatize on this issue, because the available sources contradict each other.
I personally have deep doubts that Yeshua was born on the Feast of Tabernacles (or during Passover as some others try to argue) or on any other Jewish holiday. One thing I have noticed in the Gospels is the fact that if Yeshua said or did anything on a specific Jewish Holy Day, the writer always mentions it. It would seem to me that if Yeshua was born on any specific Jewish holiday, Matthew and Luke would have mentioned it, as these are the writers who deal with the birth of the Messiah. This would certainly be true of Matthew, who was writing to a Jewish audience; he would have found this significant enough to mention. But the total silence of both Matthew and Luke in connecting Yeshua's birth with any Jewish Holy Day tells me that Yeshua was born on a normal day, therefore, the Gospel writers do not make mention of the date.