The Universal Monster Rule Gaze indicates:
A creature with a gaze attack can actively gaze as an attack action by choosing a target within range.
Being an 'attack action' (not a Standard Action), can this be used with a creature's Natural Attacks as part of a Full Attack?
No, the attack action and an attack are different things.
From the combat rules:
Attack Action: An attack action is a type of standard action. Some combat options can modify only this specific sort of action.
This means that directing the Gaze ability is a standard action. And that such creature could effectively attempt to affect a target with their gaze twice in a single round, as illustrated on this answer from 3.5 regarding gaze attacks.
