...another way that the Question can potentially cover his tracks is by making others doubt his sanity, which plays into the hallmark of the character as being inscrutable; you can't be sure what he's thinking. Again, "they" will eliminate any whom they consider to be a threat, but by making "them" underestimate you by feigning insanity is another way to throw them off your trail; this tactic has been used by people such as mob boss Vincente Gigante who, in an attempt to beat a criminal conviction, wandered the streets of Greenwich Village wearing a bathrobe and muttering to himself in an attempt to pass himself off as being too mentally unstable to be the brains of a criminal syndicate.
This could arguably be the Question's tactic here—does he really believe that aglets have sinister purposes, or is that just misinformation that he flaunts in order to make people dismiss him as a nut so that he can pursue his true agendas unmolested? ... However, just as he is in the comics that spawned him, we don't know for sure whether he's crazy like a fox or just crazy. That is the ongoing question, and it is this uncertainty that generates the character's appeal; as he once said to the Huntress: "You're drawn to my eccentric charm."