Hold on there professor!

Luke also does not NOT say it, so that comment is unwarranted as obvious. As to Christian imagination, that sounds dismissive, but can you be certain? As you said the story appears to be based on the Protoevangelium, but that is really as far as anyone can go in their assertions.
Of course, Luke doesn’t say that Zechariah
wasn’t high priest either. But as I mentioned, there is no second Temple period high priest named ‘Zechariah’ in Josephus. I know some people will claim that Zechariah could have very well been high priest during the gap in the Josephus’ record between 3 BC and AD 6 (Archelaus’ reign), but the
Protoevangelium of James, our earliest source to claim this, has Zechariah already being high priest when Mary was twelve years old.
If we suppose Jesus was born during the final years of Herod the Great (7-4 BC), going by Josephus then the high priest during that time would have been either Matthias son of Theophilus (5-4 BC) or Joazar son of Boethus (Matthias’s wife’s brother, 4 BC) - the last high priest appointed by Herod before his death.
And, if we backtrack from that some thirteen or more years (supposing Mary was age sixteen when she became betrothed to Joseph and gave birth to Jesus - as per the
Protoevangelium), we will arrive at the high priesthood of Simon (son of) Boethus (23-5 BC).
You could attempt to identify ‘Zechariah’ as actually being any of these two high priests. (You cannot count Simon, since while Zechariah was supposed to be barren, Simon actually had children - a daughter of his (Mariamne) even became Herod the Great’s third wife.) Now, Josephus does mention that Matthias son of Theophilus had a one-day replacement: because Matthias had, erm, ‘intercourse’ with his wife in a dream the night before he was to serve in Yom Kippur, a relative of his named Joseph son of Ellemus had to act as stand-in. But, even if somehow you try to identify Zechariah with Joseph son of Ellemus, it would contradict the
Protoevangelium’s scenario where Zechariah is at least high priest for four years (from when Mary was twelve up to when he was sixteen).
The idea of Zechariah being high priest is something already found in the Protoevangelium of James. It is in the 4th century that we see different Christian writers expressing that Zechariah was high priest
and received his annunciation in the Holy of Holies, either on Yom Kippur (the Day of Atonement) or on Sukkot, which they often confuse with one another. Given the widespread attestation of this belief among Christians, it probably arose earlier than the 4th century.
You might say that Luke does encourage this idea in a way, because he has Zechariah burn incense, writes as if Zechariah was the only person within the sanctuary, and mentions people praying outside the sanctuary - so automatically peoples’ minds would default to the biblical descriptions of the high priest offering incense by himself during the Day of Atonement.
But on the other hand, just because something is widely believed (and just because something has beautiful symbolism) does not automatically have to mean that it is historically factual. Luke could very well have described Zechariah’s actions
as if they were the actions of the high priest during Yom Kippur, but it’s not automatic indication that Zechariah was indeed a high priest - in other words, Luke’s possible description is more theological than literal.
Personally, I think that there is no
need to imagine Zechariah being the high priest, just because he is said to offer incense. Luke mentions that Gabriel appeared “on the right side of the altar of incense.” This altar was located in front of the Holy of Holies. While only the high priest could enter the Holy of Holies, the altar of incense is in the outer sanctuary, and is about as far as ordinary priests could go when approaching the divine. Incense was offered in the temple everyday at morning and at twilight; it wasn’t just a Yom Kippur specific event. And while only Zechariah and the angel is described in the scene, it does not necessarily have to follow that Zechariah was
alone in the sanctuary.
The Mishnah specifies that at least five priests were required for the service: those who tended the menorah - the lampstand - and prepared the altar, the one who will offer incense, and his assistant. After doing their job, said five priests would go outside the sanctuary, standing on the steps of the porch and, along with other priests, confer the priestly blessing (Numbers 6:24-26) on the people. If we suppose this tradition is accurate, then Zechariah could have been one of these five priests; the reason the people would have been surprised at his delay (1:21) may have been because only four of the five priests came out.
I am fairly sure I read somewhere that the Second Temple DID have dedicated virgins (but not perpetual virgins.)
Can you give us that ‘somewhere’?