X/Y trigger position.
mean that fallers can trigger it as well as climbers
Yes, as long as designers avoid the following edge case.
The nasty edge case that tileset designers should avoid is: You can make the button trigger's horizontal area cover exactly the wall pixels and no air pixels. This produces surprisingly skill-dependent behavior:
Climber: Pin is inside the wall and would trigger.
Faller: Pin is in front of the wall and would miss.
Builder:
I don't know if it enters the wall. Guess: It would miss. namida says: Yes, it misses.
Walkers on that builder staircase:
Enter the wall, will trigger. Do not enter the wall, will miss.
This is a result of Lemmings 1's insane placement of the lemming pin (effective coordinate) in the ground for walkers, and in the wall for climbers. Turning walkers are, for a moment, in the ground and in the wall. Oh-noing climbers are also inside the wall and thus won't fall; you can argue that this one is nice, even.
Tileset designers, please avoid this edge case. In an ideal world, you wouldn't have to pay attention to this edge case; these warning posts are a symptom of a problem in the game physics that's, sadly, strongly ingrained in core physics.
-- Simon