After giving this a LOT of thought, guess I passed on will save (some might know what I am talking about), and I decided to chime here with few of my observations and warnings, as it also involves about my character a bit as well, kind of. Not wanting to hijack this tread, I will post things about my character behind the spoilers, but is mostly there to give a bit clearer picture on what I am talking about.
I would also call out to as many players out there, to share their opinion, as well, so that both you Donny, and me, and everyone else in similar situation would get some insight on how people perceive this.
Starting with a spoiler, some ooc there, readers be advised:
While my character is not insane, there are several mental issues involved. This is something I would call "troubled" RP, and it can really be troubled to RP.
Calling this a "troubled" RP, it can put a strain on both the PLAYER RPing mental issues, as well as the PLAYERS that you would RP with. I would say most people would prefer relaxed RP, and feel the most comfortable with it, but there is just something alluring with troubled RP.
Again, possible spoilers here, readers be advised:
In case of my character, I made several rules on her creation, keeping track on how things would go in game. To keep it simple, when things went well, she would be in better mood the next day. When things got worse, she would be worse etc. Those were "short" terms differences, but there was a hidden "long" term counter in the background, that might have never been triggered at all, depending on how things would happen in game. So, now she is the way she is, and she will or will not get better, depending on her in game interactions.
The greatest problems with "troubled" RP would be in interaction with others. (caps are for emphasis, not yelling

)
First one is how other CHARACTERS perceive you, some might not want to be in your presence, for various reasons, from having bad memories from past, not carrying, or just have some sort of hate or fear from "crazy" characters. This would be IC thing only.
Second one is how PLAYERS perceive you, and this one can be more complicated. Now, I do think everyone here wants to have fun and be respectful to others, but playing "troubled" RP is bound to put you at odds with others, as sometimes, your CHARACTERS decision will NOT be the same as YOU would want them to be. Finding a limit there can be hard, in keeping the balance but still keeping it true to your character and remaining respectful. In my case, if our characters were to meet, and things would go badly, I would attempt to send a tell explaining at least a bit about the reasons. Here, I would put this ahead of immersion, even if some PLAYERS would not like that, and I know at least one person that feels the same way as I do, so,

high five to that person, and everyone else that feels the same way, and,

respectful nod to others. Some PLAYERS could be just uncomfortable with that kind of RP as well, for personal reasons or just don't like that kind of play. We are all just humans IRL, and sometimes we will miss on things that could hurt others, so is best to be prepared to that, as well.
With that said, I would also say it is a high risk - high reward situation, things would often go not the way YOU would want them, leading to something of a fiasco. In my case, when things would connect just right, it led to the most AMAZING RP episodes I ever had, making it worth the trouble. So, I say, go for it!
Next, on emoting crazy and other things. Personally, not only that I do not mind excessive emote, I actually prefer it. Why? There would often come a situation in a crowd, especially in dangerous areas with many people involved, when you don't have enough time to read everyone description in details, and some can be quite long. Emoting there gives much clearer picture off the bat, about what your characters is like, especially on the first encounter, or if there was some drastic change, for whatever reason. (Here, I would add, dark does not necessarily means evil

, but how CHARACTERS would perceive that would remain on them to figure out.) It might irk some PLAYERS, yes, so be prepared for that, if you would take that route. Taking Monk, the detective from TV show, as an example of clear mental disorder, that would probably require a lot of emote, and still would count as plausible. At what level of "crazy" to play, I can't say as I am struggling with that myself at times (I later added a part on that below)! But, I say, go for it!
Next, you mentioned your "crazy" be involved with fey pact, and that he is unlikely to brake it. That is perfectly fine, but I would advise you to think of at least one way how that could happen, certain chain of events that could lead to that, and see if them would happen! But, finally, it is your decision, on how and in what direction you want to play.
In my case, I am completely open minded. Depending on how things would go, I made a range of drafts, for her, to become anything from paladin to blackguard, from saint to ruthless murderer, from happy store keeper to cold blooded mercenary, from just what she is now to even perma death. Of course, I want her to keep on the grey light side of things, but, hey, I do not make the rules here

.
Last thing I could think of as an advice, one that could backfire at times though, is similar to what others said. When ever I am in doubt on how my character would react on certain questions or situations, I make a random dice roll for DC, usually 3d20 (for level 30 character), then try to beat it with Will save roll, as this is mental thing, with passing the roll giving better result. Kind of a way of DM-ing yourself. Not sure how that could relate to schizophrenia, maybe just to see at what level would you go "crazy" at that time, but there, just a thought. Adding randomness to mental issues kind of make a lot of sense, to me at least, and... um... even if random unexplained rolls could also annoy some people, as well, maybe, so would be good to explain them as well.
Long read, and I probably forgot about few things I wanted to say as well, but I think I said most of it.
See you on the Coast, have fun!
Started writing before your latest post, so Edit, and yes, spoiler:
"He's also not aware of his own insanity, so telling others he's insane will definitely not happen

He's often so far in his own mind that he is unaware of how strange the things he says and does actually are. Telling him about it would probably also be met with some sort of paranoia, where you are the crazy one, not him."
I know exactly what you mean!
Return what is given... one small step at the time...