We played our first game with Ghatanothoa last night and the question came up of whether the Annihilating Gaze ("Each time an investigator gains 2 or more Clue Tokens at once, he must turn a visage token faceup. If it has Ghatanothoa's face on it, he is devoured") also happens during setup when investigators get the starting clue tokens indicated on their sheets. Same goes for setting up replacement investigators when an investigator is devoured midgame.

We played without doing this, since it seemed like it would add a needless delay as investigators were drawn and devoured before they even had their first turn. But now I'm thinking that this would have the effect of making us more likely to have investigators who start with 0 or 1 clues instead of more, and limiting investigator clues is the obvious intent of this GOO power.

I know that the Dark Pharaoh herald's lose a sanity when you gain an unique item power definitely does happen during investigator setup, so maybe Ghatanothoa's power should too. Anyone here play it that way?

I would argue that you do not in fact gain clues when starting the game, your characters simply starts with them. In contrast, you do draw common/unique items at the start and therefore effects which influence or are triggered by drawing items do affect the startup as well.

Right, clues at the start of the game aren't gained. Rex Murphy starts with his printed 3 clues, and not a 4th as per his ability.

That seems like a reasonable ruling, since the Dark Pharaoh herald's power specifically states that starting equipment is included, and all the investigators who get to use their abilities during setup (Jack, Amanda, etc.) are worded "whenever [investigator] draws a card."