The only default official form of madness in the game is the insanity spell, which is a permanent confusion effect. As confusion does not affect one’s saving throws (indeed, it does not affect any of one’s numerical modifiers), neither does insanity.
The semi-official1 variant idea for madness includes one called psychosis, which does not affect Will saves in any way (it makes the afflicted chaotic evil and gives a massive bonus on Bluff checks). Other forms of madness—amnesia, multiple personality disorder, and paranoia—do, again with similarly massive numbers (−4 for amnesia and paranoia, −6 for multiple personality disorder).
Personally, I think the madness rules are pretty poorly done. The numbers are vast, which just causes gameplay problems.2 More importantly, the effects just... don’t match what these mental disorders do to a person very well.3 They’re honestly kind of offensive, in their Hollywood-esque stereotyping. Multiple personality disorder—which is more properly known as disassociative identity disorder4—is an extreme form of a mental defense mechanism, and isn’t likely to reduce Will saves, for example. Ditto for paranoia. And what losing one’s memory has to do with making Will saves, I’ll never know, but that’s certainly not suggested by the literature. Ironically, the most often stereotyped form of mental disorder—schizophrenia—is probably the one they get most right.
That said, I’m not going to recommend anything here. Frankly, my associations and experiences with mental disorders are that they’re tragic, not epic. They’re not part of my fantasy of knights and wizards. I’d strongly advise, then, that they’re not well-handled by making rules for them—they should just be roleplayed. Don’t apply penalties, resistances, immunities, or anything else mechanical—just consider them when trying to make in-character decisions. I think you’re far less likely to cause either gameplay or social problems that way.
It’s official in that Paizo printed it, but they didn’t fully detail it and it’s not an automatic part of the Pathfinder ruleset—it’s not used, for example, in Pathfinder Society play. It’s more of an idea for a GM to consider than it is a full ruleset.
Note that I have worked on third-party Pathfinder products, so I do know at least a bit of what I’m talking about here.
I’m not a psychologist, though I did take an abnormal psychology course in college, so I know at least a little bit. More importantly, I am married to a psychologist, who rolled her eyes at the descriptions I quoted to her.
Per Diagnostic and Statistical Manual of Mental Disorders (DSM-5), which defines these terms for the mental health industry. Note that MPD/DID is an extremely controversial item in the DSM-5, and a fairly large chunk of psychologists have doubts that it even exists. But if it does exist, it definitely doesn’t make sense to model it with a Will save penalty.