This wantonness therefore which occurred with Tiberius reigning I thought ought not to be passed over, so that from it the impropriety of the emperor might be assessed. For indeed the life of uprightness of a good leader is a certain rule and pattern of living for all, so the filth of an emperor is a law for scoundrels. Pilatus was sent by him into Judaea, a wicked man and putting falsehoods in unimportant matters, he encircled the Samaritans as they were going to the mountain which has the name Gadir (Gerizim) --for it was sacred to them--for the reason that he wished to learn their mysteries. And going up he outstripped the people with cavalry and infantry, he spread abroad with a contrived charge, that they had prepared to withdraw from the Romans and were seeking a place of assembly for themselves. What indeed did he not dare, who had put even Christ the lord on the cross, coming for the salvation of the human race, pouring forth upon men with many and divine works the grace of his mercy and teaching nothing other, unless that he should make peoples obedient first to god, and then to emperors? A raving man who was the servant of the madness of sacrilege, and who killed the author of salvation. And so through him the the state of the Jews as destroyed, through him there was ruin for the nation and a hastened destruction for the temple. For if Herod, who handed over John to be killed, paid the price for his treachery and cruelty (by being) thrown out from the royal power and given into exile, by how much more headlong fury is the action to be understood given (against) him who killed Christ? What was the cause of death for John I shall set forth briefly. Philippus and Herod who was previously called Antipas we showed above to have been brothers; the wife of Philippus (had been) Herodias whom Herodes unlawfully and wickedly associated to himself by right of marriage. John did not tolerate this and said to him: "it is not lawful for you to have the wife of your brother." Then the former provoked threw John into prison. And not much later he killed the just man and immovable executor of divine law. For not only as a preacher of the gospel had he blamed the incest of the brother's marriage bed, but even as an executor of the law he censured the transgressor of the law who had taken by force the wife of a living brother, especially having seed of him. Aroused by this the hatred and retribution of almost all Jews was hastened against Herod. The supporter of whom Herodias, seeing Agrippa to have had much influence with Caesar, drove him to go to Rome, where he should win over the favor of the emperor to himself, putting before him the affront of idleness, because shunning work, while he stayed at home, he allowed indignities to be brought forward against himself. For since from being a private citizen Agrippa had been made a king, how much more therefore should Caesar not hesitate that he should confer a kingdom upon him who had already long been a tetrarch. And so by no means sustaining the reproaches of his wife, he proceeded to Rome, while he was seeking the friendship of Gaius, impugned by Agrippa he lost even the tetrarchy, which he had received from Julius Augustus, and going into exile in Spain together with his wife Herodias he died from grief of mind. Tiberius having died also Gaius succeeded, who, wishing himself as the ruler both to be seen as and to be called a god, gave causes to the Jews of a very serious rebellion, and lest he should destroy the empire with a quick end, made a quicker end of the nation of the Jews. For not only did he not call his men back from illegal acts, but he even threatened those sent into Judaea with the ultimate punishment, unless they accomplished with their arms everything against justice and the dictates of religion. Agrippa was very powerful in his state, but while he wished to encircle Jerusalem with a great wall, so that it would become impregnable to the Romans---for he foresaw its imminent destruction---prevented by death he left the task unfinished. Nor did he exercise less power while Claudius was ruling, because he was also in the midst of his own beginnings, since with Gaius having been killed he had been thrust by the soldiers into the rule of the empire, the senate resisting him from weariness of the royal power, he sent Agrippa as his deputy, with whom as negotiator the promise of moderation having been given, an accommodation having been begun, a peace is agreed upon. In place of Agrippa the father Agrippa his son is substituted as king by Claudius Caesar.[Pseudo-Hegesippus 2.5]
Interestingly the MSS of Slavonic Josephus preserve the last line in a strikingly different way "he [Agrippa] himself having at Caesarea after a reign of three years having no son." One edition goes on to cite (i) Acts 12:1 - 2 (the reference to 'Herod' killing James) (ii) the end of 'Herod' at Caesarea (Acts 12:21 - 23) and then (iii) Malalas X.17.
Indeed Slavonic Josephus has a parallel chronology albeit with different material components (a) Philip has a dream where Agrippa the eagle takes over his kingdom before dying and Agrippa receiving his kingdom, (b) John the Baptist's accusation of Herod (c) 'Caesar' takes away Herod's domain and gives it to Agrippa banishing Herod and Herodias to Spain (d) Pilate's placing of the 'semaia' of Caesar in the temple (e) the crucifixion of Jesus (f) Pilate's taking money from the temple to build an aqueduct.
This arrangement is shared by all Slavonic texts however some MSS place the banishment of Herod IMMEDIATELY AFTER these events:
A short while afterward Herod went to Tiberius (begging him) so that he might honour his domain with a royal title. And Caesar was furious because of his insatiability. He took away his domain and added it to Agrippa's and banished him to Spain.
It is also interesting to quote the exact language of the narrative that follows in all MSS because of its inexactness as to the name of the Caesar in Rome.
and (Caesar) extended his wantonness against the Jews and sent Petronius
Only towards the end of the narrative does the name 'Gaius' appear. I wonder whether there was ever a Josephan narrative that supported the idea that Jesus was crucified under Claudius. It certainly doesn't exist now. But did it at one time? And was it subsequently corrected for its inaccuracies which caused Irenaeus to err? All good questions.