What of detached duty though?
There are only two centurions who show up in the gospels: one is the guy in Capernaum with the sick servant, and the other is the centurion at Golgotha.
The first centurion is most likely not a Roman one. He is more likely to have been a soldier in Herod Antipas’ army. The Herods had their own troops: Herod the Great had a multinational army made up of mercenaries and recruits from various places, which were organized among Roman lines. It’s likely that his sons also copied the Roman military structure for their own personal armies.
And because the Herods had their own military force, Roman soldiers really had no business being in the Galilee, which was Herod Antipas’ tetrarchy. Everything and everyone there was his: the soldiers, the tax collectors. Client territories, such as Antipas’ tetrarchy, were typically a source of manpower for the Romans, not additional territory for them to garrison. Roman troops were indeed occasionally supplied to client rulers whenever they faced internal or external threats, but that was the exception, not the norm. There was no serious military threat to the Galilee during the time of Jesus, so Antipas would not have needed Roman soldiers.
When Antipas got into trouble with Aretas, king of Nabataea (his womanizing with Herodias is involved here), Aretas thrashed Antipas’ army, but he did not run into a Roman legion; the legions in Syria had to be contacted first. Communications were slow though, so by the time they were ready to march, the emperor had died, orders got suspended, and Aretas got away without any impunity.
So all in all, the centurion with the ill servant is more likely to be a Herodian soldier than a Roman one. It’s also telling that John’s closest parallel to the story of the centurion’s servant is the story of the
royal official’s son.
As for Judaea, Josephus only really tells us about three incidents during Pilate’s rule, where he cracked down hard against perceived unrest. And in all three instances, it seems that it was his own soldiers, rather than legionaries, were involved.