8 Now it happened that while he was performing his priestly service before God in the appointed order of his division When was this? Gene believes it can be dated to the day. https://www.worldcat.org/title/witnesses-for-jesus-the-messiah/oclc/21426450
23 When the days of his priestly service were ended, he went back home.
24 After these days Elizabeth his wife became pregnant, and she [q]kept herself in seclusion for five months, saying
She conceived Nisan. Sixth month of her pregnancy was also sixth Hebrew month Elul.
36 And behold, even your relative Elizabeth has also conceived a son in her old age; and [z]she who was called barren is now in her sixth month. 56 And Mary stayed with her about three months, and then returned to her home.
John Is Born 57 Now the time [an]had come for Elizabeth to give birth, and she gave birth to a son. 58 Her neighbors and her relatives heard that the Lord had [ao]displayed His great mercy toward her; and they were rejoicing with her.
59 And it happened that on the eighth day they came to circumcise the child, and they were going to call him Zacharias, [ap]after his father. 60 But his mother answered and said, “No indeed; but he shall be called John.” 61 And they said to her, “There is no one among your relatives who is called by that name.” 62 And they made signs to his father, as to what he wanted him called. 63 And he asked for a tablet and wrote as follows, “His name is John.” And they were all astonished. 64 And at once his mouth was opened and his tongue loosed, and he began to speak in praise of God.
Gene suggests John born First Day Hanukkah & circumcised 8th Day.
Haftarah Hanukkah from Zechariah. https://www.blueletterbible.org/kjv/zec/4/1/t_conc_915007 Hebrew word for "Grace" relates to John's name.