You seem to desire to make my position whatever best suits your argument, MrMyth.
Or, alternatively, I'm trying to figure out exactly what your position is, rather than spend time discussing points that aren't actually relevant. So, my appreciation for the clarification below, as I think that does clear things up for me. My appreciation as well for stepping back from the other parts of the argument, which I'll take as acknowledgement that your claim about "choosing the position of a creature in a room" being an "arbitrary houserule to screw PCs" was incorrect.
if a Bodak happened to glance in the position of someone hiding in the shadows, such that the Bodak's eyes were visible to the person in the shadows, that would not be the same as their gaze meeting.
If the Bodak happened to look directly into the eyes of someone hiding in the shadows, while that person was looking at the Bodak's eyes, their gaze would meet.
Ok, this does clear things up a bit, and does seem to be the core of our disagreement. It seems to come down to two elements that I disagree with (and, if this are incorrect statements of your argument, feel free to let me know):
1) A gaze attack is only effective if the gazer and the gazee have their gazes actively meet. Simply viewing the eyes of the gazer is not enough to trigger the gaze attack.
2) If someone is hiding, but no in total concealment, and a creature looks at their precise position directly enough for their gazes to meet, this will break their hiding.
The problem with the first point is that it isn't what the rules say. Glancing at the 3.0 MM, page 8: "A gaze attack takes effect when opponents look at the creature's eyes." Same thing in the 3.5 MM, page 309. The DMG doesn't specify that, but instead is even more general, simply saying each creature within range of a gaze attack must make a save - which seems more a combat relevant description."
By the rules, if you can see a creature's eyes, you are vulnerable to its gaze attack. To claim otherwise is a house rule - that's all I've been trying to claim. If you find it fits a more mythic image or otherwise to have some sort of direct connection when eyes meet, fair enough, and feel free to run it that way in your games. But the rules support the DM in saying that all it requires is looking upon the creature's eyes, and I don't see that as unreasonable in terms of either flavor or common sense.
The problem with the second point is, again, that it isn't something in the rules. Because let's take the gaze part out of it entirely.
I am hiding in the shadows in the back corner of the room. You are standing in the middle of the room. If you declare that you don't like those shadows, and look carefully at them, what happens?
By the rules, you make a Spot check against my Hide check. If I win, I stay hidden.
Even if I don't turn my eyes away - nothing in the rules indicates that obscuring my eyes is a requirement for hiding. Nothing in the rules indicates that if I don't do so, and you look in my direction, that there is any possibility you automatically see me without having to make a spot check.
Now, you have made mention to your own personal experience with hiding, and said that the eyes are the most vulnerable part of remaining hidden. You could logically follow this, perhaps, with the idea that anyone trained in hide is automatically taking precautions to keep their eyes turned away when someone looks at them, and that if someone chooses actively to not do so, their hiding might be broken.
I wouldn't be a fan of such a ruling, myself, since I think it could arbitrarily screw PCs - but if you felt such a ruling was appropriate, you could run it that way in your games. But it would certainly be a house rule - by the rules, Hiding doesn't have any requirement to cover or turn your eyes away, nor does it give any chance for someone to automatically see you without successfully making their Spot check.
So in the end, both of the preferences you have are not unreasonable depending on the style of play you want - but both of them are very definitely houserules. And more than that, I don't think this is due to any flaw in the 3rd Edition rules - saying that gazing upon a creature's eyes renders you vulnerable to its gaze attack makes perfect sense to me, nor do I think it necessary to add more requirements and restrictions on how the rules for hiding work.
I won't object to anyone who wants to run it differently. But I will continue to disagree with anyone who insists that those rulings are by the book, or that a DM who runs them differently is at fault or a "bad DM".