Weeell I do have a psychology degree but that's quite a long way from being a qualified psychiatrist, which is a medical profession. I'm not even a "practicing psychologist"

.
My dad (now retired) worked in mental health for over 30 years, though.
So I'm as unqualified as most, really, slightly more knowledge but all "book learning". That said, I can tell you for a fact that the notion that he has schizophrenia or any other schizoid disorder is utterly ridiculous.
I don't think he's mentally ill. I do have quite a bit of knowledge about (childhood) autism though, and I have mused over the fact that he has a few indications of being on the mild end of the autistic spectrum; his social ability isn't entirely "normal", he's very literal (despite using constant metaphors) and he also occasionally "stims" (self-stimulation when agitated) - he often bounces his leg up and down in the diary room and he does a bit of jaw-clenching at times which can be (although isn't necessarily!) an indicator. He has quite a few hallmarks of someone who is UNdiagnosed with mild autism and has
learned social conventions to cover it as he's aged. This may well be what Dan identified as "an awkwardness that he can't put his finger on".
Autism is not a mental illness, though, in my opinion.