[Just mythoughts]

Luke 1:5. The “course of Abia”, ends around what we now call the month of June. Around the thirteen day. John the Baptist was conceived after the priest Zacharias finished his course. John the Baptist was in the womb 6 months when Mary conceived Christ.

[BipolarBob]

That is not a time. That is the division of sons of Aaron.
When in David’s time the family of Aaron was multiplied, he divided them into twenty-four courses, for the more regular performances of their office, that it might never be either neglected for want of hands or engrossed by a few. The eighth of those was that of Abia (1 Chr. 24:10 ), who was descended from Eleazar, Aaron’s eldest son.
Jesus was born spring or summer when the shepherds were out tending flocks and/or sheep were birthing.