Josephus on Pentecost
The writings of Josephus on Pentecost indicate that he did not reckon Pentecost using the Lunar Sabbath method of counting seven weeks and then an additional fifty days.
Josephus writes in Jewish Antiquities III, after describing the sacrifice required for the Wave Sheaf Offering:
When the seventh week following this sacrifice has elapsed—these are the forty-nine days of the (so-called) “Weeks”—on the fiftieth day, which the Hebrews call Asartha, the word denoting “fiftieth,” they present to God a loaf of two assarôns of flour of wheat made with leaven and, as sacrifice, two lambs. These are by ordinance to be offered to God, but are made up into a repast for the priests, and it is not permitted to leave any portion of them over for the morrow.[1]
It should be clear from this description that the timing of Pentecost from the Wave Sheaf Offering is seven weeks (or "forty-nine days"), and that Pentecost is then on the fiftieth day. He specifically says here that "the (so-called) 'Weeks'", referring to the name "Feast of Weeks", are composed of the forty-nine days and not counted separately.
Josephus also writes in The Wars of the Jews:
Now when that feast, which was observed after seven weeks,and which the Jews called Pentecost, was at hand, its name being taken from the number of the days, the people got together, but not on account of the accustomed Divine worship, but of the indignation they had.[2]
Here Josephus tells us that Pentecost was observed after a count of seven weeks, not a count of seven weeks and then an additional fifty days. He then clarifies that the name Pentecost is taken from the number of days (50). If Josephus was using the Lunar Sabbath Pentecost calendar (where the fifty days are counted after the seven weeks), he would have referred to Pentecost as the feast "observed after fifty days", not after only seven weeks.