His troops moved north and occupied Babylon and Seleucia probably sometime in 127 BC, when the Parthians were fighting nomadic invaders in the eastern part of their territory. His rule there must have been short, however, for the Parthian governor of Babylon and the north, Himerus, was back in Seleucia and Babylon by 126. Himerus could not have been a rebel, since he struck coins in the name of the Parthian rulers Phraates II and Artabanus II, both of whom were killed in fighting in eastern Iran. Himerus abused his power and is said to have oppressed the cities of Mesopotamia, plundering them and killing their inhabitants. Cuneiform documents from Babylon stop after this date, indicating that the city did not survive the depredations of Himerus.
as far as i am aware babylon ceased to effectivly exist sometime during the classical era
Babylon was an immense ruin, so large that tought its site wasn't forgotten historically, you had to wait the XXth century to have enough ressources dealing with.
The population living there made a speciality of seeling it, brick after brick.
Rebuilding a city there would ask for not only building something, but clean a large surface, repair or more like build irrigation canals from scratch (as the rivers bed moved), rebuild houses, etc.
The best you'll have would be the fundation of a brand new city that would use the ancient materials at disposals there.
If you really need another city to be taken from ashes, Seleukia would be a more sensible choice.
And still, you had regular, while not continuous, settlement up to the High Middle Ages.
think that was sporadic settlement by rural peasants or such. never really a functioning city per se after that