I still follow the thinking of In The Labyrinth on trap detection. No trap is impossible to detect, but it may be very very difficult / unikely to detect.
But the fact something is thought of as a trap is different from the actual thing.
Also, the fact someone is thinking of searching for a trap is different from what they actually perceive.
So when someone says they are searching for a trap, they are searching for signs of a trap, and they get told what they see, which may or may not be something that is a trap.
Someone with a skill that gives an extra ability to detect traps will have a broader mindset of what to look for, and will get their perceptions described differently.
So I think about the actual situation in deciding how to set the chances of detection, and how to describe what the PC notices. Thinking of the bell trap, someone could maybe discover it either by looking from below through the crack with enough light while slowly opening the lid, or by maybe hearing or feeling an extremely faint sound or vibration of the bell moving before it rang, if it's very quiet and they can concentrate and aren't wearing gloves or a helmet or whatever. It also might be a very appropriate time to ask exactly what the PC does and give them a hard chance if they're peeking the right way, and a nearly-impossible chance of the other way unless they're extremely sensitive and the conditions are right. But even if they do detect it, what they detect is just a sense of something else moving or making sound other than the lid, unless they're actually seeing the bell (but they might only see part of the bell first if they're being careful, and not able to see what it is without opening it more.
Usually with traps, people are going to see something of the mechanism, something that could be or seems like a mechanism, and not "oh you can tell it's a trap that will do X if you do Y". And they may also get a lot of false positives, but people with trap detection skills may also be skilled at testing them more safely, though all of that will tend to take some time, too.