It would have been preferable had you given a clearer citation for Antiquities of the Jews; the "250-252" appears to refer to line numbers of some kind, which various translations of Antiquities of the Jews do not mention at all. A better way would be to mention the book, chapter, and section, as those are found in all translations (in this case, book 3, chapter 10, section 5), or if someone wanted to be really specific mention those and the numbers.
On this, the standard citation for Josephus is book/index, not book/chapter/verse. The abbreviation is Joseph. and the works are
AJ (
Antiquitates Judaicae – or
Antiquities of the Jews),
BJ (
Bellum Judaicum – or
Wars of the Jews),
Ap. (
Contra Apionem – or
Against Apion), and
Vit. (
Vita – or
Life [of Josephus]). Some editions lack the index. The ones of significance do not; Loeb and Whiston editions for example.
However, while Josephus refers to the tradition of counting from the 15th, he never actually uses the word Sabbath in this passage (available
here, for the record--the first translation I consulted did not have the line numbers, but this one did, or at least lists some of them). I am not aware of people in
Greek using the word Sabbath for this meaning. (it is also possible this idea only developed after the writing of the New Testament, as I do not think we have direct evidence of it before Josephus)
This is because he's not referencing the Sabbath. He's referring to the count to Pentecost, which begins on the 16th.
But on the second day of unleavened bread, which is the sixteenth day of the month, they first partake of the fruits of the earth, for before that day they do not touch them. And while they suppose it proper to honor God, from whom they obtain this plentiful provision, in the first place, they offer the first-fruits of their barley, and that in the manner following: They take a handful of the ears, and dry them, then beat them small, and purge the barley from the bran; they then bring one tenth deal to the altar, to God; and, casting one handful of it upon the fire, they leave the rest for the use of the priest. [ . . . ] When a week of weeks has passed over after this sacrifice, (which weeks contain forty and nine days), on the fiftieth day, which is Pentecost, but is called by the Hebrews Asartha, which signifies Pentecost, they bring to God a loaf, made of wheat flour, of two tenth deals, with leaven; and for sacrifices they bring two lambs; and when they have only presented them to God, they are made ready for supper for the priests; nor is it permitted to leave any thing of them till the day following. (Joseph.
AJ 3.250–253 or Book 3, Chapter 10, 5–6).
The "idea" goes back to before the Hasmonean period. From the 8th of Nisan to the close of the festival, mourning was not permitted. According to the Scholiast to the Megallit Ta'anit, this was to commemorate the Pharisaic victory over the Saduccees concerning the start of the Pentecost count (i.e. whether the count should be from the day after the holy convocation, considered a holiday Sabbath, or whether the count should be from the day following the weekly Sabbath). The Pharisees won, and the count was codified as beginning on the 16th, which Josephus, an actual first century priest, confirms, as noted above (Schol.
Meg Ta'an. 1b).
The problem with this assertion is that if it was to avoid confusion, it didn't at all. Every writing I am aware of we have from the earlier centuries interpreted this Sabbath (the day after the crucifixion) as occurring on Saturday.
Precisely! No one ever got it confused, until modern-ish times when people started trying to finesse the text of the gospels to support an erroneous Wednesday or Thursday crucifixion. When Matthew says that the next day was the day that followed the preparation, no one ever got it confused throughout the centuries. Everyone agreed that he meant Saturday.
So, I would have to disagree with you that it failed in its goal to avoid confusion.
A major issue I have with the idea that the Sabbath referred to was not Saturday and was a separate day from the weekly Sabbath is that it would seem very odd for the Gospels to not clearly specify this fact, such as adding "this was not the weekly Sabbath, but Nisan 15, which counts as a Sabbath". Surely they knew there were non-Jewish people reading it who would simply associate the Sabbath with Saturday.
It's worth pointing out in this instance that we are discussing Pentecost. The Gospels are in no way unclear that the Sabbath following the crucifixion was Saturday. The point of confusion we're discussing is the count to Pentecost, which began on the 16th. The confusion that has been interjected into this scenario is that some are trying to suggest a Wednesday or Thursday crucifixion. To do that, there has to be a Sabbath on the day following, and the only way to satisfy this requirement of the narrative is to suggest that the 15th was the Sabbath intended.
As you say, if
that is what they meant, surely there would be some explanation. But the Gospel accounts aren't trying to educate us on the particulars of the Pentecost tradition of the first century. They are telling us that Jesus died on the day of preparation, and the day after was the Sabbath. There's absolutely no reason for any of them to step back and break down the a-b-cs of how the Pentecost count was carried out.