I can't quite read your diagram, but considering that we know from GURPS that Tireces, Moagim, Moagim Reborn, and Alric are all reincarnations of the same soul (Tireces and Moagim being the same person as well), and we know Balor is Connacht, then the cycle seems to go like this (call Tireces/Moagim/Reborn/Alric "A" and Connacht/Balor "B"):
1st Era - Evil B (good B returned) kills good A (evil A reborn), then dies. Dark Age.
2nd Era - Good A reborn kills evil B reborn, then disappears. Light Age.
3rd Era - Evil A (good A returned) kills good B (evil B returned), then dies. Dark Age.
4th Era - Good B reborn kills evil A reborn, then disappears. Light Age.
So each spirit/person follows a pattern of evil-win, evil-lose, good-lose, good-win, and the two spirits' patterns are offset by two eras (so when A is evil-win, B is good-lose). Whenever someone is Evil, whether win or lose, they are not only their own spirit but also posessed by the Leveller, who is ALWAYS evil EVERY time, but loses half the time.