Ye Olde Inn

The gargoyle is supposed to be a trap trigger in quest 1. However, you can also unleash those three rooms at whim. Had I given up the lure of invincibility by not moving, I probably could have divided the heroes with the goblins and the gargoyle. Instead, the gargoyle was predictable and easy as usual, with the old "hey you can't hurt me until I move" thing. The heroes were fully prepared and disarmed the trap. If I had moved the gargoyle ahead of this, the trap would have been disarmed for them...

What did y'all do? The heroes actually found this quest really fun to my surprise. I thought it was going to be an easy quest with nothing game breaking or new, if not boring. I had planned to run it with quest 2, but they took the whole game time playing the first one.

The quest notes say the gargoyle only comes alive when the chest is opened without the trap being disarmed... and I would go by that for the most part.
However if the trap is successfully disarmed and the heroes appear to be doing well by the time they clear out the middle room; your last line of defense to stop the heroes is that one lonely Fimir by the door.
If the heroes are doing exceedingly well at this point and the quest hasn't been challenging enough, I'd have no qualms with waking the gargoyle once they open the door out of the middle room. You could pull out the Fimir to halt their progression and chase after them with the gargoyle.
However if they're close to death at this point, you could leave the gargoyle out. As Zargon, you want to make it challenging, but not kill them off.