As the player has lost his investigator and also is eliminated from the game (i.e. he does not get a new investigator), the player is out. Therefore there should be no more turns "at his regular position". So the clock rotation only takes place one last time at the end of the turn of the death of the player's investigator.
Am I wrong?
Sorry to say you are wrong in this case. The FAQ is trying to make clear it is the opposite of what you think.
What exactly happens when an investigator is devoured
while battling the Ancient One?
A Doom token is added to the Ancient One’s Doom track
as usual, and that player is eliminated from the game.
Note, however, that the clock is still advanced during that
player’s “turn,” even though he has been eliminated.
and here again :
If an investigator’s death awakens the Ancient One, does
that player get a new investigator?
No. However, the clock still advances during the
dead investigator’s “turn” during the battle with the
It means that every "day" in battle with Ancient, every turnover of clock hand, until at least one investigator alive, every "dead" investigator must move clock hand again in his "turn" ? Or just once, in turn when investigator become devoured ?
What the FAQ is trying to say is that while the investigator is out of the game and not replaced, the player is still in the game. The player still has a turn, all he does is Advance the Clock (because he has no investigator to Attack the Ancient One), but he still has his turn.
In general, the rules don't really differentiate between "the player" and "the investigator" because most of the time there isn't a difference but in this case it matters. The player is still in the game, it is just that he doesn't have an investigator anymore. Since he doesn't have an investigator he can't Attack the Ancient One, but he can (and must) still Advance the Clock.
4 Player game, Clock is on IX at the start of Player A's turn. Doom track has only one space left before the Ancient One awakens.
During his turn, Player A's investigator is devoured.
A Doom token is added to the Doom track! Ancient One awakens. Trigger any Ancient One awakens Attack (for Ithaqua and Yig only).
Player A does not get a replacement investigator but he still has to Advance the Clock.
Since it is now Midnight (XII), the player now have to resolve the Ancient One's Attack.
Ancient One now attacks all the remaining Investigators (there are only 3 now), belonging to Players B, C, and D.
Assuming the three remaining investigators survive the attack.
Player B has his turn, Attacks the Ancient One, Advances the Clock to III.
Player C has his turn, Attacks the Ancient One, Advances the Clock to VI.
Player D has his turn, Attacks the Ancient One, Advances the Clock to IX.
Player A has his turn, does nothing except Advances the Clock to XII (Midnight).
Ancient One now attacks all the remaining Investigators, belonging to Players B, C, and D.
And so on.
The example I gave also highlights the point that when the Ancient One awakens, the clock is not reset but continues from where it was. This means that the Ancient One can attack before some, or all (in the example above), of the investigators get a chance to attack the Ancient One themselves.