A key thing to remember about traps: perception merely tells you that something is there, not anything about it. That is what investigation is for, and a poor roll on that could easily set off the trap.
That point aside, perception should be used to reveal things like "you notice a scuff mark along the floors and ceiling next to the wall, some discoloration in a pattern, a thin wire running across the hallway, a floor tile that appears to be a pressure switch of some kind, or a groove in the wall/floor. It is up to the players to decide if such descriptions mean a trap and precisely what that means as a trap. Scuff marks on the floor in ceiling could be a secret door or early some sort of crushing wall trap, a thin wire may actually be the key to opening a secret door or it could release a falling boulder, a floor tile may shoot a puff of poisonous gas, or it may just light the next room or could even be a meaningless switch (or broken trap).
Want to mess with them? Put an obvious chest at the end of a hallway filled with traps. Make the chest locked, but untrapped and empty. If you REALLY want to mess with them, make the traps self-resetting so they have to go back through them again.
The point is to play with player expectations. Give them descriptions and find ways to not be consistent or simple with your traps. Maybe the trip wire helps to hide a floor switch behind it (thus a higher DC to perceive)? And remember to use every sense. An electric floor tile may not have anything visual, but maybe they can hear an electric hum, or feel the hair on their skin rise statically as they near it. Traps need not be impossible merely serve as obstacles to slow or deter players.
One method would be to put the trigger far away from where the characters are when they trigger it, such as a domino effect or Rube Goldberg machine. Perhaps a dark room/hall has something very sensitive to light, so that when the light appears, it triggers the effect (light can be seen from much farther away than it provides even the dimmest of light). Air pressure and sound are other potential things that can be used from a distant before the party could become aware of the trigger.
Another would be be for the party to see the trigger at the same moment they activate it. For example, pulling open a door pulls a wire attached to the other side of it, which fires a crossbow at the person who pulled the door open.
Finally, you could disguise it that there's no actual trap, simply bad decisions that lead to bad things. For example, a sealed container actually has poisonous gas, so opening it exposes the character. Explosive Runes are another common example of this. It's not actually a trap, so the only way to avoid it is to not do what PCs normally do.
The thing with traps is that they can be made undetectable easily enough - there may be no way to see a weak spot in the floor but there are a couple of things to consider.
First, how to the inhabitants of the area bypass the trap? If they never stop on square X, that may be detectable as an oddly dusty spot or excessive wear on only one side of the corridor.
Second, and perhaps more important, is it fun? I'm not talking about just fun for you but fun for the whole group. DM gotchas* may be fun for you but does it make sense and will it be fun for the group. Don't punish players for their PCs doing things when they have no possible reason to expect danger and no possible way to avoid it.
*for example: "Ha! You just fell into a vat of acid that you had absolutely no chance to notice or avoid and take 3,000 point of damage! Bazinga!"
I would second what was said above. Just making the DC to notice anything a 50 or something and it becomes undetectable. But if it takes the fun away from the players then how cool is it. Things can be hard and maybe above the level for the PCs to be there, but it is up to the DM to make things fair. If something is above the PCs heads and you point it out, then they can all die if they go there. It is not fun to make a dungeon to lead the PCs into where they have no right being in, same for a trap where they have no chance to find or disarm.
You can have something like a trap that is tied to a portal and the PCs need to go into it for the adventure to start. You need to strongarm them to get the adventure going. It is not how I like to DM, but as a player I can get onboard and take this choice away from my PC. Kind of like the adventure where the PCs need to be captured or be placed in prison. I think that most DMs try not to force the PCs actions.
Put the mechanism of the trap inside the wall, construct a 3" thick lead panel in front of it, and place a normal façade in front of that, aligned correctly with the rest of the wall as the PCs see it.
Any spell will fail to find what is hidden behind the lead. Now you just have to be an artisan in the construction and home decoration industries, to fool mortal senses.
Have an invisible hidden Imp by the trigger mechanism for the trap. The trap is set off whenever the imp decides to pull the lever. And the Imp is 120' away in magical darkness (100' tall ceiling or very large room or long corridor).
I would suggest that you stop playing semantics because it's not actually fun.
That said, I would also ask you why you need to do that. My guess is that you are trying to defeat a divination spell, and which divination spell you are trying to defeat is very much material to the answer.