Some other possible sources (not checked) might be:
The Chronicle of John Malalas
The Chronicle of Marcellinus Comes
The Ecclesiastical History of Evagrius
John of Ephesus (monophysite), Ecclesiastical History (surviving part 521-585) and Lives of Eastern Saints
The challenge is to find a source or else to show that the tale is apocryphal, but I appreciate this is a tricky one

Best wishes,
Andrew