Use a passive check
Passive checks are designed for this kind of situation, where a PC is attempting something over and over:
A passive check is a special kind of ability check that doesn't involve any die rolls. Such a check can represent the average result for a task done repeatedly, such as searching for secret doors over and over again, or can be used when the DM wants to secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster.
Time may be important
Keep in mind that in an escape room there is usually a time limit. If played in D&D, players may have other things to do that sit there Searchingsearching the room over and over again - they do not have unlimited time. Each Search attempt is time that could be spent sharing and comparing clues, discussing solutions, looking more closely at specific objects, etc. Examining existing clues and developing theories will aid in further investigations.
Investigation needs context
Remember that investigation is not perception. Even though the character sees that there are two pens on the desk, they may not realise they are suspicious or important until they find out that the killer wrote a note in ink. They need the context to understand what kind of clue they are looking for. The pens can be found with perception immediately, but until the players realise the pens are important, investigating them won't turn up anything. Once the killer's note is found, an invesitgation check may deduce which pen is the right one.