This post is necessarily incomplete but there are some supporting ideas below.
1. "The Magicians": Nero is one of the Magicians (False Caesars) who fool the people. He is probably the Elymas in Acts:
Suetonius, 12 Caesars, "Nero":
"19. He planned but two foreign tours, to Alexandria and Achaia; and he gave up the former on the very day when he was to have started, disturbed by a threatening portent. For as he was making the round of the temples and had sat down in the shrine of Vesta, first the fringe of his garment caught when he attempted to get up, and then such darkness overspread his eyes that he could see nothing..."
Acts 13: 8 - 11 (RSV)
 But El'ymas the magician (for that is the meaning of his name) withstood them, seeking to turn away the proconsul from the faith.
 But Saul, who is also called Paul, filled with the Holy Spirit, looked intently at him
 and said, "You son of the devil, you enemy of all righteousness, full of all deceit and villainy, will you not stop making crooked the straight paths of the Lord?
 And now, behold, the hand of the Lord is upon you, and you shall be blind and unable to see the sun for a time." Immediately mist and darkness fell upon him and he went about seeking people to lead him by the hand.
This Set Piece finds Elymas given as "You son of the devil, you enemy of all righteousness, full of all deceit and villainy..."
Nero's Bio-Dad was that Type of evil who once ran over a man with his chariot killing him because...You know...Because...
"28. Besides abusing freeborn boys and seducing married women, he debauched the vestal virgin Rubria. The freedwoman Acte he all but made his lawful wife, after bribing some ex-consuls to perjure themselves by swearing that she was of royal birth. He castrated the boy Sporus and actually tried to make a woman of him; and he married him with all the usual ceremonies, including a dowry and a bridal veil, took him to his house attended by a great throng, and treated him as his wife. And the witty jest that someone made is still current, that it would have been well for the world if Nero's father Domitius had had that kind of wife..."
This particular "12 years" in the Acts of Peter may indeed point to Nero. It also contains a curious Symmetry with 12 years prior to the Fall of the Temple:
"13: I may fairly include among his shows the entrance of Tiridates into the city. He was a king of Armenia, whom Nero induced by great promises to come to Rome; and since he was prevented by bad weather from exhibiting him to the people on the day appointed by proclamation, he produced him at the first favourable opportunity, with the praetorian cohorts drawn up in full armour about the temples in the Forum, while he himself sat in a curule chair on the rostra in the attire of a triumphing general, surrounded by military ensigns and standards. As the king approached along a sloping platform, the emperor at first let him fall at his feet, but raised him with his right hand and kissed him. Then, while the king made supplication, Nero took the turban from his head and replaced it with a diadem, while a man of praetorian rank translated the words of the suppliant and proclaimed them to the throng. From there the king was taken to the theatre, and when he had again done obeisance, Nero gave him a seat at his right hand. Because of all this Nero was hailed as Imperator, and after depositing a laurel wreath in the Capitol, he closed the two doors of the temple of Janus, as a sign that no war was left anywhere..."
This is all found in Annals, Book 15. Nero is indeed a "Magician": Corbulo is a Main Character in all of this (See: "Aeneas" in Acts - the 12th Legion.).
"13. Meanwhile in Rome, memorials of victory over the Parthians were being erected, and arches in the centre of the Capitoline Hill, all having been decreed by the Senate while the war was ongoing, and which were not abandoned now, truth being ignored in favour of appearances. Indeed, to hide his own anxiety as to the situation abroad, Nero had old grain, which had spoiled, thrown into the Tiber to show that there were no fears for the corn-supply. Nor was the price raised, though some two hundred vessels had been wrecked in harbour by a violent storm, and a hundred more which had navigated upriver were destroyed on the Tiber by a chance fire..."
As I state, this is not complete but is in keeping with the Roman Historical Patterns of the NT rewrites. More Analysis may be needed here.
PS: It, of course, should be realized that "Peter" here could not POSSIBLY be the Peter of the Gospels.