Stop fantasizing for Red John being a Jane's second personality.
At least out loud.
This is rant, not an educational post (expect lesson 'Don't be an ableist.').
The overwhelming majority of systems' representation is 'they're a (serial) killer'. It's actively harming systems and you're using people's suffering as your amusement. You see systems as this mysterious, mystical, interesting, kinda exotic, not entirely human being. You see them as a useful plot device, to use as you please, to add this mythologic being, to amuse yourself. It's so sickening.
People with DID/OSDD/P-DID and so on are real people with myriad experiences. Associating them with being a serial killer, an abuser is ableist and disgustful.
And you can't just spawn an alter, so Jane would need to do drugs or have a condition, physical or mental, to have 'second personality' (which isn't a second personality in reality, more like a hallucination, and people with hallucinations also aren't serial killers). But for you and other people it's the same, you know nothing and just stop being an asshole using people's suffering to please yourself.
For short films with good representation I recommend 'Petals of a Rose' and 'Alter' by Bugambilia Films (both on YouTube).