GM question about gaze universal monster ability

So as part of some monsters I am making, I am making a Mythic hydra but I want to swap one of the mythic abilities for a gaze attack. The published mythic hydra selected for its mythic abilities, the standard mythic power, dual initiative, bleed and push. So my question is if I want to swap out say push for a gaze attack, does that give the hydra one type of gaze attack or can I give each head a different gaze attack. The reason I am asking is since if one type of gaze attack is given per selection, I can only give three gaze attacks at most by swapping out the rest of its abilities except for the mythic power ability

You are the GM so you can do whatever you want, this kind of falls under rule Zero. The only thing you really need to worry about will this make the hydra too powerful for your players. Another concern would this make the hydra powerful enough to justify an increase in CR. The Cr increase is only relevant if you are using normal XP rules for character advancement.

You are the GM so you can do whatever you want, this kind of falls under rule Zero. The only thing you really need to worry about will this make the hydra too powerful for your players. Another concern would this make the hydra powerful enough to justify an increase in CR. The Cr increase is only relevant if you are using normal XP rules for character advancement.

Ah I see then maybe will just switch bleed out for some gazes. It shouldn’t change the CR or make it too difficult since it would be switching a little more consistent damage for some save abilities that my party should make. And they do know that this hydra is dangerous to look at so they probably will take some precautions. Thanks!

don't forget that Gaze attacks happen on the players turn, and potentially on the monsters turn as well.

So, if you have a 10 headed hydra, each with a gaze attack, each player will need to save 10 times on their turn, and then the hydra can force 10 more saves on it's turn.

and While a character can somewhat avoid the gaze attack by using blindfold or averting their eyes, they aren't foolproof.

Univ Mon Rules: Gaze (Su) is both an attack and a defense
...Each opponent within range of a gaze attack must attempt a saving throw each round at the beginning of her turn in the initiative order. ... then
A creature with a gaze attack can actively gaze as an attack action by choosing a target within range. That opponent must attempt a saving throw but can try to avoid this as described above. Thus, it is possible for an opponent to save against a creature’s gaze twice during the same round, once before the opponent’s action and once during the creature’s turn.
no mention of the number of heads or eyes.
With the above and a high BAB, the creature with 3 attacks could attempt 3 gaze attacks. So no benefit from taking it twice.

As others pointed out, a gaze attack usually is independent of the number of heads or eyes. While a specific creature could have a unique or modified ability, it would have to be carefully balanced or be more like ray attacks. While I can't easily speak to beholders or eye tyrants (since it's hard to get their stats now), I believe for a while there were limits on how many eye beams and such could be directed at one creature, but again, those aren't necessarily gaze attacks.

In the case of a unique hydra, you could make a gaze ability that added +1 or +2 to the DC for every head the creature focused on a target, probably giving up a bite or attack, but with something like a hydra, which might have 5 to 12 heads, that's likely to just ramp the DC to almost unfair amounts to paralyze someone and then, next round they're dead. Or the creature has to maintain focus with each of the heads, but balancing it all out would be the key. Normally it's just a single check, as long as the creature's eyes could be seen.