You can catch a serial killer by.... being a useless detective but going on a date with someone, who happens to slip some bit of evidence that it is them. the detective is the serial killer and finds out by looking in the mirror by speaking to some mad person who happens to know it all, but gives cryptic clues, and they give some kind of weird nonsense clue that suddenly clicks. Depends what kind of story you want to write.
My problem with the Korean revenge movie is that most serial killers are obsessed. They don't retire and take it easy until the statute of limitations runs out. My problem with the amateur detective solving the case is one of how he's going to have access to the crime scene to collect forensics, how he's going to do the legwork to track down a list of suspects, and then to trim that down to the killer...and then how to trap him into admitting his guilt/how to produce evidence that will convict him. In the "Yorkshire Ripper" case, he started by trying to exact revenge upon a prostitute who'd cheated him by committing GBH on another prostitute. His GBH got more and more extreme until it became murder. The first four of his victims survived, one actually identified him (she noted the number-plate of the van he got into, being driven by a friend), but the case was dropped because the victim was a known prostitute and didn't want to press it - her husband was doing time for assault... Sutcliffe was arrested and questioned nine times before he was finally charged.
That would be a nice little twist, unless we're reading the story from the sick detective's perspective. Both would be interesting perspectives.
There's just been a story on this topic over at A Story in 100 Words. http://entropy2.com/blogs/100words/2015/11/23/the-setup/ (I'm not 100% sure on the rules for posting links. Is this OK?)
Imagine you're reading it from the perspective of the detective when he is in control of his mind. Then he finds out there is a side he doesn't know about.
There is a theory that says a criminal will always take something from a crime scene, and will always leave something behind. It could be something like leaving a single hair or skin under a victims fingernails. If you're 6'2" and you drive your 5'3" victim's car...don't move the drivers seat. Likewise, killers pick up fibers and other evidence that will show they were at the scene. Be it hairs from the victims cat or pollen from a unique genus of flowers grown in the area of the crime. There is many a slip twixt a cup and the lip.
Yes the suspects and killer will be supernatural but they don't use witchcraft to do killings because magic always leaves a trace due to their wands being registered to a specific witch. Witches aren't allowed to use other witches wands, just as witches aren't allowed to use spells from another witches spell book, unless through verbally granted permission. Witchcraft have strict rules. That's why killers use knives and other hands-on methods to commit crimes. But their will be smart and well calculated killers in the vein of "Hannibal" (not man eating doe lol), who will use other witches wands and spell books etc to commit they crimes.
Try the Secret Window angle. Rainy goes around killing the people around him, and has no idea that he is John Shooter until the end. Fairly neat twist in a thriller type story. Rainy has multiple personality disorder, so when the conditions are right he becomes John Shooter. Neither knows the other exists until he stumbles onto an old memory that finally forces him to accept that he and John Shooter are the same person. Just an idea that seemed to work in a movie. Could be reworked to fill your application in some way perhaps.
Maybe have the killer, kill on particular dates like the movies eg Halloween, Christmas, Friday 13th etc etc. Geek out on it. Maybe as the film killings happen the police find clues similar to the movies, so can plot killers next step, could lead to chase scene. Maybe the police track any suspects by name-a-likes, Wes craven, John carpenter etc?...
