Just to be clear, you are shifting the goalposts quite a bit.
The original argument is:
1. Sneaky PC looks into room which contains a bodak.
2. DM tells player that PC must make a save vs. the bodak's gaze attack.
3. I say that this is a case of bad DMing, as the DM failed to take the circumstances into account and arbitrarily chose the result most likely to screw the players.
4. The counter-claim is that the DM should not be faulted for going by the book....implying or outright stating that the RAW claims that anyone who sees a bodak must save, based on the first bullet point under "Gaze Attacks" in the DMG (or SRD replicating that bullet point).
Interesting, but... not quite accurate.
The claim was made that
because the rogue was hidden, the Bodak was thus unlikely to be looking in its direction. Some considered this to be a common sense situation where the rules should be overriden. You took it a step further, and said that by the very rules themselves, the DM was going against the rules in having the player make a save.
To argue that point, you didn't make the argument that he made a bad and arbitrary call - you made the claim that his call was against the rules, and that going by RAW, the Bodak's face couldn't be visible from his viewpoint. You later revised this claim to instead be that he couldn't meet gazes with the Bodak while hidden, and that if he could, he would no longer be hidden.
There's a couple claims in there I disagree with.
One, that whether the Bodak's face is visible is in any way connected with him being hidden. It isn't. The DM could decide the Bodak's positioning based on any number of factors, or use random chance to determine it. In this case, he was informed by the adventure of its position and that its responsibility was to watch the entrance for intruders - elements that, given the window the rogue was looking from, resulted in its features being clearly visible to him.
If you feel that was a bad and arbitrary ruling, fair enough. I simply find it strange, though, since after so many arguments in favor of a logically consistent setting, you would prefer a DM make a ruling solely on a metagame element and a desire to softball things for the player.
5. This is shown to be an incomplete reading.
6. A claim is made that any other reading is "house ruling", apparently even if consistent with the RAW.
The rule say that "A gaze attack takes effect when opponents look at the creature's eyes."
You, and others, have made the claim that the gaze attack only works if those involved actively meet each other's gaze. Some claiming that is the more mythic way for such an ability to work. Maybe, maybe not. Either way, though, it is not how the rules clearly state it works, which means your reading is absolutely a house rule.
7. I then claim that, if determining whether or not the rogue meets the bodak's gaze is house ruling, so too is merely claiming that he does so arbitrarily.
Again, the original claim that I labelled a house rule was that because a rogue was hidden, this implied that the Bodak wasn't looking in his direction. This
is a house rule. Putting the issue of gaze attacks entirely aside, you can hide from creature's looking in your direction as long as you have cover or concealment.
Every time I have raised this point, you've instead abruptly stopped responding to that portion of the argument, or called it an unrelated topic and tried to switch the focus of the discussion.
You were the one who claimed that it was "a house rule, at best" that a rogue looking in the window would be subject to a Bodak's gaze. There was no connection to that statement and any claim on my behalf that whether the rogue meets the Bodak's gaze was a house rule.
Note that by making that claim, you aren't just saying that it isn't likely for a creature to meet the Bodak's gaze - you are, again, saying that it is outright against the rules. That there is something in the rules such that it is not possible for a hidden character to meet a Bodak's gaze.
Despite not having, at any point, put forward any evidence for this - and having been presented with several pieces of evidence that directly contradict such a position.
Now, it may be true that "By the rules, if you can see a creature's eyes, you are vulnerable to its gaze attack" if "vulnerable to its gaze attack" is taken to mean "are in a position where you might have to make a saving throw."
The specific context of the rule, though is looking "the thing in its eye" and catching "the thing's eye". Neither of these mean "can see the thing's eye". If you equate the two, that is a house rule.
Here is the actual rules quote, one more time: "A gaze attack takes effect when opponents look at the creature's eyes."
It does not get clearer than that. You are trying to add additional restrictions to this by making the claim of context. The quotes you have provided? Are from a descriptive narrative giving examples of characters being affected by a creature's gaze attack. That flavor text helps show how the ability works, yes, but it does not override the actual rules themselves.
Here are what seem to have been the core arguments that have been made, and here are my barebones objections to them:
Claim: If you are hidden, it means the opponent is most likely looking in another objection.
Rebuttal: No, since if this was true, you could automatically spot a hidden figure by declaring that you are looking at the shadows in which they are hiding - which is not the case. Instead, even if you look at their hiding spot, you make a Spot check opposed by their Hide check, and if you fail, you do not see them unless you in some fashion remove or negate their concealment or cover.
Claim: A gaze attack requires actively meeting the gaze of the creature, not simply viewing its eyes.
Rebuttal: No, a gaze attack simply requires viewing its eyes, based on the opening line of the gaze attack entry in the monster manual, "A gaze attack takes effect when opponents look at the creature's eyes."
