When did Zachariah depart from Jerusalem to his home?
Zachariah and his wife had longed for God to give them a biological child (Luke 1: 13). News from the angel that God has granted them should have made Zachariah happy.
The news would eliminate disgrace his wife in the middle of Israeli society, which looked down on barren women (Luke 1: 25). As his response, Zachariah went home soon after completion of his task.
And it came to pass, that, as soon as the days of his service were accomplished, he departed to his own house. (Luke 1: 23)
Zachariah did not wait for dawn. He traveled Jerusalem–Hebron night dangerous trip in 6 BC century for the sake of immediate reach home and broke the news to his wife.