The gaze rules are kind of... a mess. For one thing, the Dungeon Master’s Guide and Rules Compendium disagree on the action necessary to actively use a gaze (DMG has it as an attack action; RC has it as a standard action separate from the attack action); see here for the confusion and controversy around RC supplanting core.
For another, the rules clearly do not consider the possibility of a creature with more than one gaze attack at all. This makes it very difficult to deduce how things are “supposed” to be. I will offer a pedantically-literal rules-as-written analysis, but with the caveat that really, it seems clear to me that the rules just don’t consider this situation at all and really you should ask the DM.
Passive Gaze Attacks
Each character within range of a gaze attack must attempt a saving throw (which can be a Fortitude or Will save) each round at the beginning of his turn.
This statement makes no distinction between where the gaze is coming from; just forces all creatures in range of any gaze to make a saving throw against it each round. So if there are two gazes, each character is making two saving throws each round. The two gazes do not interact at all.
Active Gaze Attacks
A creature with a gaze attack can actively attempt to use its gaze as an attack action [RC: standard action]. The creature simply chooses a target within range, and that opponent must attempt a saving throw.
The issue here is “its gaze.” Is that the gaze attack referred to in the previous sentence? If so, then the creature has to choose a single gaze attack to focus on a target. Or is that just the creature’s gaze, which includes at least one gaze attack but possibly more? If so, then the creature has to roll... a single saving throw against all of them? After all, the rules as “a saving throw.”