Feast of the Dedication (15th day of the seventh month).
I challenge you to find any reference anywhere to Hanukah being held on the 15th day of the seventh month. (Reminder: The word "hanukah" means "dedication".)
What did Josephus say regarding the order of King Herod of the burning of Matthias and his companions alive for raising the sedition? It happened on the night before the fast, and that very night, there was an eclipse of the moon (Antiquities, Book XVII, Chapter 6, Section 4).
That it happened on the day of "a fast". It's generally accepted to be the eclipse of 4 BC.
A lunar eclipse happened during a full moon. Fred Espenak of NASA said that in 33 BC when Jesus was born, there were two lunar eclipses: April 1 and September 25 (Julian calendar dates). I chose April 1 because it is observed in Jerusalem.
Of course, there's a problem, because Josephus has a bunch of events in it that could be verified from secular sources, and if the eclipse referred to byJosephus was in 33 BC instead of 4 BC, all of those dates would be off.
What are the Jewish fasts in the 15th of the month? Nothing except the Fast of Esther on Nisan 15.
Except that the Fast of Esther was never observed on Nisan 15.
ETA: And wait. Where did the 15th come from? Josephus doesn't say anything about the 15th.
During the reformation of the Jewish calendar, the Fast of Esther was moved to Adar and Passover and Feast of Unleavened Bread were placed in Nisan.
Except that the Mishnah places Passover in Nisan, and it was completed almost 200 years before calendrical reform.
And of course we could go back to Constantine and note that a lot of Christians put Passover in Nisan, which was also before the Jewish calendar reform of 358. Constantine seemed to think that all of the Jews put Passover in Nisan. (And of course, he was correct.)
Feast of the Dedication should be in Tishri 15
Says who? The earliest reference to it is in the Book of Maccabees, 500 years before the calendar reform, and it is firmly on the 25th of Kislev, and you will not find any reference anywhere that puts it on any other date.
So it was moved on Kislev 25 (to compete with Christmas on December 25?).
Which would be even odder, since the calendar reform happened outside of the Roman empire at first, and the date of Christmas wasn't set at December 25 until after that time.
These prove that the Israelites were using two calendars during the crucifixion of Jesus: a purely lunar calendar and a lunisolar calendar. When they reformed their calendar in 358/359 AD, they incorporated Passover and other feasts in the former to the latter and stopped using it.
But the Torah says they were only using one calendar. Leviticus 23 again. So you would have to say that that calendar was purely lunar, despite the barley references, and then they moved some, but not all, of the holidays to the lunisolar calendar, and then they moved the rest later.
Oy Vey! I can only imagine the arguing in the synagogues when they tried that.
Another aside: You seem to think that the Egyptians used a purley lunar calendar. If so, they didn't record that use. Everything about the Egyptian calendar, including their religious festivals, revolved around the Nile floods. A purely lunar calendar would have been quite useless.