If the author of Mark thought Joseph could be a sympathetic figure
and that this Joseph was Caiaphas (and that the "high priest" unnamed in Mark is not sympathetic), then he might not have known the history of the period very well, because "the high priest" (who is not named in Mark) pushes the execution forward.
That's a lot of if's, of course.
The weakest point is the claim that Joseph called Caiaphas = Joseph of Arimathea in the Gospel of Mark.... i.e., the point of this thread.
Antiquities 18.
After him came Annius Rufus, under whom died Caesar, the second emperor of the Romans, the duration of whose reign was fifty-seven years, besides six months and two days (of which time Antonius ruled together with him fourteen years; but the duration of his life was seventy-seven years); upon whose death Tiberius Nero, his wife Julia's son, succeeded. He was now the third emperor; and he sent Valerius Gratus to be procurator of Judea, and to succeed Annius Rufus. This man deprived Ananus of the high priesthood, and appointed Ismael, the son of Phabi, to be high priest. He also deprived him in a little time, and ordained Eleazar, the son of Ananus, who had been high priest before, to be high priest; which office, when he had held for a year, Gratus deprived him of it, and gave the high priesthood to Simon, the son of Camithus; and when he had possessed that dignity no longer than a year, Joseph Caiaphas was made his successor. When Gratus had done those things, he went back to Rome, after he had tarried in Judea eleven years, when Pontius Pilate came as his successor.
Antiquities 18.
But when this tumult was appeased, the Samaritan senate sent an embassy to Vitellius, a man that had been consul, and who was now president of Syria, and accused Pilate of the murder of those that were killed; for that they did not go to Tirathaba in order to revolt from the Romans, but to escape the violence of Pilate. So Vitellius sent Marcellus, a friend of his, to take care of the affairs of Judea, and ordered Pilate to go to Rome, to answer before the emperor to the accusations of the Jews. So Pilate, when he had tarried ten years in Judea, made haste to Rome, and this in obedience to the orders of Vitellius, which he durst not contradict; but before he could get to Rome Tiberius was dead.
3. But Vitellius came into Judea, and went up to Jerusalem; it was at the time of that festival which is called the Passover. Vitellius was there magnificently received, and released the inhabitants of Jerusalem from all the taxes upon the fruits that were bought and sold, and gave them leave to have the care of the high priest's vestments, with all their ornaments, and to have them under the custody of the priests in the temple, which power they used to have formerly, although at this time they were laid up in the tower of Antonia, the citadel so called, and that on the occasion following: There was one of the [high] priests, named Hyrcanus; and as there were many of that name, he was the first of them; this man built a tower near the temple, and when he had so done, he generally dwelt in it, and had these vestments with him, because it was lawful for him alone to put them on, and he had them there reposited when he went down into the city, and took his ordinary garments; the same things were continued to be done by his sons, and by their sons after them. But when Herod came to be king, he rebuilt this tower, which was very conveniently situated, in a magnificent manner; and because he was a friend to Antonius, he called it by the name of Antonia. And as he found these vestments lying there, he retained them in the same place, as believing, that while he had them in his custody, the people would make no innovations against him. The like to what Herod did was done by his son Archelaus, who was made king after him; after whom the Romans, when they entered on the government, took possession of these vestments of the high priest, and had them reposited in a stone-chamber, under the seal of the priests, and of the keepers of the temple, the captain of the guard lighting a lamp there every day; and seven days before a festival (13) they were delivered to them by the captain of the guard, when the high priest having purified them, and made use of them, laid them up again in the same chamber where they had been laid up before, and this the very next day after the feast was over. This was the practice at the three yearly festivals, and on the fast day; but Vitellius put those garments into our own power, as in the days of our forefathers, and ordered the captain of the guard not to trouble himself to inquire where they were laid, or when they were to be used; and this he did as an act of kindness, to oblige the nation to him. Besides which, he also deprived Joseph, who was also called Caiaphas, of the high priesthood, and appointed Jonathan the son of Ananus, the former high priest, to succeed him. After which, he took his journey back to Antioch.
According to the Antiquities, this Joseph who was called
Caiaphas held the high priesthood for the entire duration that Pilate was around. And for a fairly long time too (circa 18-36 CE).
The high priesthood was nearly a family business (or oligopoly) in the first century AD, with the prefects perhaps taking a cut and threatening to put another family in power temporarily if they don't get their bribe (else why the keen interest on their part as Romans?):
Wiki-
Joseph was the son-in-law of Annas (also called Ananus) the son of Seth. Annas was deposed, but had five sons who served as high priest after him. The terms of Annas, Caiaphas, and the five brothers are:
Ananus (or Annas) the son of Seth (6–15)
Eleazar the son of Ananus (16–17)
Caiaphas - properly called Joseph son of Caiaphas (18–36), who had married the daughter of Annas (John 18:13)
Jonathan the son of Ananus (36–37 and 44)
Theophilus the son of Ananus (37–41)
Matthias the son of Ananus (43)
Ananus the son of Ananus (63)
This last one got the boot in the mysterious 20.200.
"... almost every critical biblical position was earlier advanced by skeptics." - Raymond Brown