Grimrock

I would say that secret buttons make sense as parallel progression or for secrets, but not as things standing in the way of core progression. That is, secret buttons should generally not be necessary to find in order to complete the dungeon, but finding them should garner a reward - be it being able to bypass a part of the dungeon, gaining access to additional loot, making an encounter easier, etc. If there are secret buttons which are chokepoints of advancement, the search area should be fairly well-constrained. In general I'd say that secret buttons should be relatively close to whatever they influence - sufficiently that the player can see what has changed from pressing it, or at least hear it. It's also good to use things to hint that there may be a secret nearby, even if its not necessarily a button (an example of this was in the sewers level, there were a lot of 'how do I get to that ledge with the glowing fragment?' sorts of things).

I also think that establishing some sort of pattern to their use is part of the game when using secret buttons. In Grimrock, part of that pattern is that there's only a few variations, so you can learn to look for them efficiently. That aspect of 'learning' - learning the biases and patterns of the dungeon - is what makes mechanics like that rewarding IMO. Essentially its not 'oh, I happened to look up at the right time', its more like 'this looks like the kind of place the dungeon would have there be a secret button'. For instance, one theme in Grimrock 2 was that whenever you have something that tries to force you through an area quickly - spike traps, water, etc - there was almost always a secret button hidden somewhere inside. That kind of recurring theme is generally a good to use in other places as well to give a feel of cohesion, but its especially important when using non-obvious game elements.

The absolute worst design would be to have a progression-necessary secret button in a complex maze of similar-looking, long passages, which controls something very far away from the button's location - and for that to be the only secret button in the dungeon.

Yes, that's true. I always make sure, that the player can notice what has changed when pressing a button (well 95% ;-) ) and that the secret button is within a reasonable range to what it changes (1-6 fields for most of the time). But I think it's still fair to have them for a path or a puzzle that's obviously part of the main path as the player can search a few wall when he notices something is missing or doesn't work out as expected.

For normal secrets:
I search every wall in a dungeon crawler campaign and then finding something powerful without a hint is extremely rewarding. :-P

I use secrets button quite often, even as a main progress "point". I realize many nowadays player do not like it and I perfectly understand your opinion as well. However as nimnay said - Grimrock is a tribute to older dungeon crawlers and intentionally carries over many of the aspects that are considered bad design today.
Secret buttons just somehow go with old dungeoncrawlers and I do not see why not to use it. Of course if you will not use it in your mod, there is definitely nothing wrong.

I think that secret buttons add a certain atmosphere to crawling around a dungeon, but I definitely like there to be some sort of logic or hints as to where they are placed. I am certainly not going to search every wall in a game like LOG2 for the hope of a secret button but I like it when you get a subtle clue that there is a secret area around (a note, a monster behind a wall, an off-looking wall, etc) and then you can search a limited area for a button and find one.

For the most part the LOG games do a good job of kind of training you to think where the secret buttons are, and the fact that there are only a couple of types for a each wallet makes it easy to scan an area pretty quick. I agree that the sokoban-type puzzle which required you to find a secret button to complete it kind of annoyed me too, as I wasn't in "secret button" finding mode when looking for it.

Overall, I definitely like secret buttons for secret areas and treasure (in moderation), but prefer a minor hint that there is "somewhere I cannot reach" before finding one. In terms of main story progression - I definitely agree that secret buttons used on their own to block story progression should be minimal AND definitely within close proximity of the door they open. In general, I really dislike puzzles where you have to walk 10 spaces, push a button, walk back to see what it did, then walk back to the buttons. The puzzle should be fun but when there is a lot of walking around involved it just wastes my time. If there is any sort of trial and error involved, it should be about that process, not walking back and forth - so make it all very close together!

I don't use secret buttons for anything but secrets. Meskia will not have them in puzzles.