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Let's say you have a very paranoid party, who have reason to be paranoid, and are very carefully exploring every 5ft square for traps. Nobody was a Rogue, but someone did have Trapfinding.
They come across a 5ft square where a trap will go off in... But the trap itself is located in the next 5ft square. Something like:
PXT
P = player, X = square (trap will affect this square), T = trap (trap mechanism is here but set to trigger when X is occupied.
I wasn't sure how to handle it when I came across it so I judged it as a 'you have a gut feeling that stepping forward would be a very bad idea'.
How would you have handled it? And how should I handle it in the future?
In your specific example, I would treat both squares as containing the trap.
I get as creative as possible when describing traps.
First of all, I try not to describe the successful perception test as "finding a trap". I describe a detail a phenomenon that was noticed with perception that the player can then extrapolate the presence of a trap.
For example, if square X was to be the target of a gout of flame, and square T was the flamethrower — if the player tells me they are searching square X I would (upon a successful roll) tell them that they saw "traces of scorch marks and signs of immense heat". If they searched square T I would say "You see a cleverly concealed nozzle, and the suggestion of a panel that runs down to the floor directly beneath it."
An emphasis on square-by-square trapfinding really spoils the game for me, and I think it ruins the pace of the game for my players. They like knowing that for some traps, they get to "spot" them as a mere perception check, but they still have to "figure out" the trap themselves.
It's not the RAW, but it is more fun this way.