Those gnostics had a very long lifespan Jerry.I'm not sure, then, how could Josephus be writing about Basilides? And, how could Vespasian meet with Basilides? Vespasian died in 79 AD, and the Antiquities was finished about 94 AD.
Could there be more than one person named Basilides? And if Josephus is writing about an earlier Basilides, perhaps that person isn't connected with the later Saturninus?
The 'late' Basilides aside, we're already spanning 3 generations of Origins process, unless one wants to skip such as Tiberius ... and/or that other Pandera. Perhaps such as 'Basilides' is more a title as I have speculated for 'Chrest' the 'good', and the same for 'Christ' the 'anointed', but as his son Isadore was apparently his successor, then this seems less likely.
It appears that both Basilides's and Valentinus's systems were a subsequent strata of 'gnosticism', more Hellenized than the prior, what I'll call the Egypto-Judaic system. Here, it is interesting that 'Basilides' means 'royal' or 'kingly', similar to the NZR Egyptian root that I believe is the basis of the Biblical 'Nazarite'.