tl;dr: I mostly use this sort of declaration to guide narration. Not all information is equally hide-able, and direct, mechanical benefits for generic, player-dictated rolls can be problematic.
Different information has differing flexibility for being hidden behind dice rolls
What I do varies a bit by situation, specifically what the player is looking for and what there is to find. My players tend to make "called" investigations like this in a few situations:
- They are looking for mechanical information (like traps, signs of enemy movement, etc. which will help them survive or conserve resources)
- They are looking for roleplaying-specific information (it matters for their character, but not for advancing or surviving the game)
- They are looking for plot-specific information (clues or events which move the game story forward)
Of these, I have found that it tends to be troublesome to withhold too much information on the latter two: plot information is necessary for the story to advance, and roleplaying information is usually important to players self-defining their fun in the game. Especially for plot information, it is undesirable for players to (unknowingly) define themselves out of finding it.
That sort of consideration really limits how much of a "penalty" you can apply to investigations of areas, however focused or unfocused.
There is, however, one thing I keep in mind for "called roll" situations: players do not get to dictate outcomes or successes when proposing actions. Saying "I check for traps" does not make a character any better at recognizing traps, understanding mechanisms, or anything like that. Try going outside and spending fifteen minutes digging random holes without any goal in particular. Then repeat but with a specific goal of looking for buried gold nuggets. I bet you'll find that wanting to find gold really doesn't change anything about the process, nor does it change how much gold you find.
The only exception to this that I've found meaningful is when there is limited opportunity to search, commonly a time limit or some scarce resource used in the searching.
Degrees of success
I frequently use the "degrees of success or failure" model of interpreting dice rolls in D&D 5e, and it seems especially useful for players that try to powergame (for lack of a better word) like this. Since a disguised trap could look like basically anything (or nothing!), even a search for traps, specifically, a trap-searcher will still need to make a pretty expansive investigation.
Degrees of success make it possible to convey information incompletely, which is very useful for a situation like the one described in the question. A floor tile might look out of place, but not be part of a trap. Or it might be part of a trap, but the specifics of what that trap is are unclear.
If a character is so focused on traps that they barely notice other points of interest, those others might get brief and intriguing mentions but no more details. I like having the flexibility to make sure that vital information is conveyed, but not necessarily highlighted or fully explained in the moment. Particularly if the PC's attention is fixed elsewhere.
Player declarations of what they are thinking about are important for narration
A player that wants to look for traps is concerned about traps! Whether or not I would consider giving some sort of bonus or penalty to their examinations, the narration is more trap-themed: I emphasize dangerous looking pieces of the environment and the uncertainty surrounding the entire situation:
The bas relief carvings on the wall seem like they have a lot of sharply cut stone details-- they're definitely sharp enough to cut flesh. The uneven stones paving the floor make each step seem ominous, and they somehow all seem out of place! The damaged ceiling above the far door looks almost like it could come down at any moment.
If someone wants to find indications of traps, lots of things might look trap-related enough to capture their attention. Unless it's an excellent roll, I find it best to not give definitive, binary information (that is a trap, and it looks like it will drop a swinging blade!). Players can still learn enough to be cautious, and their investigation is still helpful in making the situation safer than it might otherwise be.
Ad-hoc modifiers can be tough to work with
While I do sometimes fiddle with roll details in the course of the game I resist doing it in this kind of situation. It can be difficult to know in advance how much an arbitrary +/-3 will shift the distribution of roll outcomes, and you might end up virtually guaranteeing success or failure without meaning to. When I do want to adjust this sort of thing I generally adjust the DC of the check. It's easier (for me) to remember how tough a DC 10 is vs. a DC 15, keeps the math easier (and therefore faster and less error-prone), and is still invisible to players.
It is also tricky to allow players to unilaterally declare such a modifier, especially just because they asked for it. "I look for traps" giving a +3 for trap detection is only a short hop away from "I try to land a hit" in combat giving an arbitrary bonus to an Attack roll.
If you really want to let players get a benefit out of focusing their attention in this way, and especially if you want there to be a corresponding impediment (+3 for traps, -3 for anything else, for example) I'll recommend 5e's Advantage and Disadvantage mechanic. You could, for example, call for a roll of 2d20, taking the higher roll for their focus and the lower for anything outside of their focus.
I've never used that two-rolls-in-one mechanic, but I've definitely used the "roll 2d20" without explaining why. My players have been excited to know that there is something unusual going on, but not knowing what it is, or even if it is to their benefit or not.