Nearly all historians agree with the 4 BC date. Only W.E. Filmer argued for 1 BC. And Timothy D Barnes refuted Filmer.
—
The 1 b.c. date makes more sense because the total lunar eclipse of Jan. 10 was much more notable over Jerusalem than that of 4 b.c.
The 1 b.c. date places the birth of Christ on June 17, 2 b.c., when Venus and Jupiter merged in the sky (in Leo), the only time that has occurred in recorded history.
Jesus would have been a toddler on Dec. 25, 2 b.c., when the astronomers from the East visited him and did not return to Herod.
On the night Friday, April 3, 33 a.d., the moon rose engulfed in a total lunar eclipse again over Jerusalem (a blood moon, in Virgo), indicating a full life led with a sacrifice.
Gaius Caesar, Augustus’ adopted son and heir was present in Rome and participated as a member of his father’s consilium at the time when, following the death of Herod, Archelaus and Atnipas travelled to Rome to appeal their rival claims to the throne of Judea (refer to Anthologies xvii 9.5)
Gaius departed Rome in 2 BC and spent the next several years travelling in the east. therefore, Herod could not have died in 1 BC.
Regarding your point about the lunar eclipse - it would make sense to look at the evidence provided by the Megillot Ta’anit, a Jewish list of days on which, by reason of notable events associated with them, the Jews were not allowed to fast. The list was complied shortly before the destruction of the temple in A.D. 70, and the reason for the holiday is given in every case but two. S. Zeitlin explains that “undoubtedly the chronicler’s silence in these instances is due to their being recently instituted holidays pro tempore. The incidents being well know to all, it was not necessary to add any explanations.”
ccording to Jewish tradition these holidays, which fell on 7 Kislev and 2 Shebat, commemorated the death of Herod and the death of Jannai, both kings who had died within recent memory and whom the Jews hated.
Now 7 Kislev, which the Jewish commentator actually preferred to associate with Herod, fell earlier in the year than any of the above three lunar eclipses, and for this reason it must be ruled out. But 2 Shebat, although it fell before the eclipse in 4 B.C., occurred fifteen days after eclipse in 1 B.C. In view of the serious deterioration of Herod’s health which Josephus says set in immediately after the eclipse, it does not seem likely that he could have lived much longer than the fortnight that this allows.