If you're struggling with motivation, and you want to go the "He's just crazy" route, you might be able to solve the problem by showing why he's crazy. If he was born crazy, in a 'Michael Meyers/Halloween' sort of way, then show the first time that craziness came out. Remember, Michael Meyers butchered his sister at the beginning of the film, and that was enough. You have to establish his personality in some way, or else the character will feel thin and unsatisfying.
Special Agent Pendergrast just jumps in and starts solving things (why? Because his family is crazy!) Jack Reacher? We know he doesn't like bullies, bureaucracy and BS, but why? Is there any motivation in a Vince Flynn novel? Nope, Mitch Rapp is just a Dudley DoRight who's out to preserve the American way. End of story. Lucas Davenport is a police officer. He solves crimes, because that's what he does. Harry Bosch is one of the world's greatest characters, but why is he such a tough, never give up bad ass? Sure, after innumerable novels we get some motivation lightly sprinkled over the top, but the stories wouldn't be any worse if this wasn't included.
When you're dealing with series characters like Reacher, their motivation doesn't matter all that much because they are reflection characters. Reacher's job, besides kicking ass and nailing the girls, is to act as a window through which the reader absorbs the story and views the other characters. You might not know what drives Reacher to sneak into the the mob bosses mansion, but it doesn't matter because the story isn't about Reacher. The story is about the little girl the mob boss is holding captive, and her worried mother sitting at home. You learn (through reacher) what motivates the other characters in the story, and they're who the story is really about. Reacher discovers that the mob boss became a psychopath after his only son was gunned down by a rival mob, and when he discovers that motivation, so do you.
The old detective novels did this all the time. Ross Macdonald, who IMO is the best detective novelist who ever lived, never said more than a few words about his detective, Lew Archer. But when he did, it spoke volumes. The one instance that sticks out to me was when a character told Archer that she'd heard about him. He asked what she'd heard, and her response was, "I've heard you're a very lonely man."
That was it.
But through Archer, readers were introduced to such a wide range of characters, all completely round and bursting with personality and motivation, that readers devoured the books. They were what the books were about. Archer (like Reacher and Bosch, etc) are just tour guides.