Even during that blank period, I do not see the Magisterium suffering a non mage being their ruler.
The Magisterium was not filled with mages during that time period... officially, anyway, a lot of power is run by houses and it is possible that while a non mage relative held the seat, that relative was being ordered by a mage relative. It was in Storm, which was 7:00-7:99, that then allowed mages to publicly take office.
At least this is what the Codex Entry: The Imperial Chantry implies.
Edit: Which is kind of strange, as in that same entry it said the "Black" Divine was established in Towers, which is 3:00-3:99, who was a male and part of the Circle. So, mages can take leadership positions with religion, but couldn't with politics, officially, until 400 years later... okay...
Edit2: I do wish a dev would help correct some of the things in this thread, I sometimes wonder if I'm wrong in my current understanding of the lore.