Sorry to revive this topic, but if you still need an opinion, I would ask you: what is exactly that "searching" used for? Is it A)"searching for hidden objects" or B)"general searching the room?"
If A) then, I would say make it a thievery skill. Usually it is thieves the ones who are more trained to search for hidden traps, treasures and the like.
If B) then it is a too general action to be considered a skill per-se. It is more like "describe me the room" or "search some something that is not too hidden". It is then a normal action like "walk", "eat", "quaff" and the like.
Then, if you want the player to actively search for traps/treasures/hidden chests/... then I think you could have, in the one hand, a skill that is "detect hidden" inside "thievery" skillset, and in the other hand, a skill general action called "search" to just look for general things around.
And in general, as for myself, I always consider a "skill" some action that only certain people can do successfully with training (like sorcery, 1st aid, fishing, playing an instrument, whatever), and a "normal action" something that most of the people do without training (even when if you train you can do it a bit better), like walking, selling/buying, observing (search?), and so on, and besides that, it is something that is done most of the time.
And even that, "normal actions" i think they depend more on your basic stats (STR, AGI, INT, ...) than on the skill itself. For example, a high AGI could improve how well your character can walk better, but there is nothing like "walking training". Or your PER(ception) can increase your character attention to detail when he is "general searching", but there is nothing like "the school of searchers" that trains your @ how to observe your environment.
And if you think about "searching" as an action/skill to look for resources (kind of like a bushcraft skill), maybe you can use it as a general action, but that its outcome is affected by PER(ception) stat, since rangers and bushcrafters are so good at perception, but they dont have a specifit training just to "search". Everyone can "search" in the forest, and many people will easily discover common resources like wood or rocks, but people with more PER will discover more things useful things.
Hope that was helpful.
Good luck with your project.