From a game perspective, yes, of course traps should have tells. These are games about choices. Without choices to make, traps are just time/resource sinks.
From a verisimilitude perspective, no, of course traps should not have tells. Traps are placed to scare, harm, and hinder people. Giving them tells defeats the entire point of traps.
It's all down to which of those is more important to you. Game play or verisimilitude.
Even from a game-play perspective, a tell isn't always necessary; sometimes the point isn't the choices to be made as to what to do about the trap but more what to do
after the trap has been set off.
One of my favourite traps is the one-way chute trap where the first (or first few, if not in single file) character falls through an unseen or illusion-covered hole in the floor and winds up, usually unharmed, somewhere on a lower level in the dungeon*. (think
Get Smart and how Maxwell arrives at work every morning)
Now there's lots of choices for those stuck above: do they intentionally follow their companion(s) down the now-obvious hole, do they keep exploring and hope to reunite elsewhere, do they spend time and effort trying to fish their companion(s) back out of the chute, if such is even possible, or ???
Meanwhile, whoever is stuck down below might have problems of their own and certainly has choices to make: try to get back up the chute, stay put and hope for rescue, carry on exploring alone, or ???
* - or maybe even teleported away somewhere else completely, I've done that one too.
Other than that I'm all about what makes sense in the setting. A new or well-maintained trap might not have any tells whatsoever. A long-abandoned trap might have started to show signs of its presence, or fail to function properly if-when triggered. That said, a long-abandoned trap might also have fewer tells than it once did as any clues to its existence are now under a thick layer of dust.
Unlike some here, I'm fine if they move at a snail's pace searching every square inch for traps, as that's what cautious characters would do.