Note: I'm operating on the assumption that 187!Tyki =/= 155!Tyki =/= 109!Tyki. 187!Tyki is, for starters, insane by a lot of counts. The following are elaborations on that fact. If they sound weird and become AU later on, I can roll with it.
1. He smiles more. Unless you are family, whereupon he'll either ignore you as he usually does or you can top him into eternity kind of hilariously. But if you're an Exorcist, he will usually be smiling in your presence. He has absolutely zero interest in humans now unless the human in question is strong in some way that pings him. Mindreaders, strangely, will find that there's no actual happiness behind the smile! It'll feel almost like being zen, except it's constantly pleasure all the time. Tyki's officially awakened as the Noah of pleasure; there's a human side left to him but it's diminishing by the day. Which leads to...
2. His obsession with the remnants of his white life. He's not as interested in humans anymore, but he's aware that he's changed and is interested in how much of a change has occurred. So far he's tried fishing, smoking... neither of them really do it for him anymore. This annoys him! He will not discuss it and will smile (especially if you are an Exorcist, SEE #1) at you if you ask, but there's a definite >/ quality when it comes to the stuff he doesn't enjoy that he should enjoy. On the one hand, he's kind of grown out of it and it's OK because he's grown into better things. On the other hand, it's a loss and he will be mildly fuckish with other versions of himself if they have it and he doesn't. Only if they actively get into it before him, though.
2a) This isn't to say that he'll refuse a smoke. He won't! It's hobo instinct that you can take a smoke and trade it later on, and it's habit from the other life that smoking makes him feel good (or at least feels better than not-smoking). So he does. But it makes no real difference to him.
3. When you lose interest in one thing, your fascination with others intensifies. It's a lot easier for him to kill someone than it used to be! He still won't do it if they're not a challenge, especially in the DR, which is full of Exorcists just waiting to have their hearts torn out, but it takes a lot less. "You have Innocence" is now an excellent reason to kill someone. People are mostly saved from this due to the fact that he knows that they just come back to life, and Devit told him that their Innocence tends to come back too. He jumped rather quickly to the conclusion: then you have to make the Innocence reject them, make them fall, because as far as he knows, there is no way to come back from that. The Innocence isn't your fickle girlfriend, it will not take you back if you bring it flowers. But that requires an entirely different kind of fucking with people. He's willing to do it! It just... takes him longer because he's not Rhode and most of the people he picks on are Allens and therefore kind of resilient.
4. You can generally tell whether he's interested in fighting at the time or not depending on whether there are Tease around. The Tease are the closest sign he has to admitting that he misses the way things used to be. He doesn't need them to fight anymore, which I theorized back when 187 first came out but canon seems to back it. He blocked Kanda's sword with his arm. His fighting's gotten a lot simpler and also a lot more dangerous. And he loves it, but simultaneously he feels the absence, so he bred the Tease over the course of a few months but only brings them out when he needs something non-battle-y done. Of course, most people will not interpret it that way, but he doesn't care either way.
5. The DR makes his CR a little weird. It takes a lot more than it used to need to make him notice people, especially with all the doubles around. Rhodes always top him, Cyrils and Wiselys always make him wary, and Allens always interest him. The rest... tends to fall under the branch of 'sorry, should I remember your name?'
6. He doesn't wear the suit anymore! Neither does he wear the hobo outfit. Actually, it's kind of hard to tell him apart from the modern!AU Tykis (are there any in the DR?) because he settles for jeans (they're comfortable, OK?) and whatever shirts he picks up out of the general laundry. He's started doing this more of late. But those outfits were... designed for a specific identity. Which he doesn't quite fulfill anymore. And OK, he could wear the hooker outfit, but why would he? Not that he really thinks about it in those terms, but that's how he feels.
7. Since he's still being consumed by the Noah, he doesn't have a consistent schedule because sometimes he's attacked by fits of Noah's memories! They hurt, except for the part where they don't really because, hurr, pleasure. Except they do, again, because that's his humanity getting torn out of him. =/ He doesn't like to talk about them. The scars are OK to talk about because they're obvious, but he won't mention the fits and if other people notice, he'll probably turn the subject back on them and get more vicious if they bring it up. HEALTHY COPING TECHNIQUES.
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general CR post
Allen: Arguably, Tyki's feeling on any Allen starts off complicated and gets simpler depending on their AU type. He likes his own cheating boy and still does, because the factors that made him like Allen didn't change. Allen is a savior, a good person and just enough of a rebellious brat to be funny. In another life, they really probably could've been friends. Liking Allen comes easily to him! But the human part of him hasn't completely disappeared. It's still being consumed slowly by the Noah, and that part of him /hates/ Allen for the memory of what he can never go back to. It's probably the most he's ever hated anyone. Being Tyki, he likes the duality of the feeling! Ironically, it's the Noah that stops him from acting on it. Noah's Pleasure means that he basically operates these days in a constant state of zen, where everything's fun and amusing. So he acts on the fact that he likes Allen! And hating him means that he also enjoys seeing him squirm! He'd kill Allen given two pence, but doesn't bother because it doesn't get him anywhere, and mindless hate is boring. He'd probably be kindest to the weakest Allens. The stronger Allens he'd build up in an effort to take their Innocence.
Himself: ... not his actual State Of Opinions On Himself, but how he feels on other versions. In this case, it heavily depends on what timepoint they come from, and whether it's apparently obvious. Tyki does not go around looking for reasons to be bitter! If a version of himself isn't hoboing around, he won't wonder whether they can and will treat them the way he treats everyone else: depending on their reactions. In hobo cases... he'll try to behave normally, but there will always be flashes of something wrong. Because he envies them, but Noah's memory buries the feeling, so he's left with this odd sense of... pity and loss and envy for what he knows is coming to them. It wouldn't occur to him to act on them; he doesn't have that much empathy left in him, but he feels it nonetheless.
Rhode: Being a Noah, oddly, doesn't strengthen Tyki's family feeling. It's different for Rhode. He's always liked her best of the family, and the fact that she stayed with him when he hit that patch of awakening makes him like her more. But this is on an overall level. On a daily level, it's kind of like "... god, she's topping me again. Why is she topping me again." He's more likely to go along with what she does than he used to be! But, typical Rhode, she still has moments of making him go ":|...." She's the height of all things Noah for him.
Wisely: As a rule, Tyki doesn't like being easy to read. Wisely compounds this by being family, and considering Tyki still has a lot of thoughts that still aren't in line with the Noah Way, he likes the fact that Wisely can read his mind even less than he would, say, an Exorcist doing it. Buuut Zen Principle downgrades his dislike to a sort of mild annoyance, and then only whenever Wisely's around. Wisely gets the weirdest mix of his dis/honesty, because if the guy can read his mind anyway, why bother trying to hide it? It's not like there's much left to hide. ... And then sometimes he just likes to make Wisely's life hard, so he tries anyway. :|b
Cyril: Sob. SOOOB. ... Actually, aside from the VIRULENT ATTEMPTS AT INCEST, Cyril doesn't disturb Tyki all that much. Mostly it's just a matter of "why are you trying to touch me there, didn't anyone ever show you on the doll, that's a Bad Place, stop that. 8|" He likes the fact that he can foist Rhode off on his brother and take off! ... of course, then there are the times where Cyril touches him and... yeah, no, take your kisses and get out.
The Earl: Whatever else, the Earl is the boss of him, and Tyki knows it. This doesn't mean that he goes along willingly, or has stopped telling the Earl that he's fat. It's his way of conveying the fact that on the human side, he always found the Earl a little creepy, and it combined with the blank Noah fealty into becoming the sort of way you'd tease a fat uncle. He still goes along with the Earl more because it entertains him than anything else. The Noah simply makes sure that his priorities are more likely to align with the clan's these days.
Devit: Devit kind of falls in the category of family Tyki doesn't really care about when they're out of sight. He'd help Devit out of a pinch because they're family and also Devit would probably bitch hilariously about how no one asked him, stupid hobo! THAT WAS HIS FIGHT DFamily: It... depends. Family doesn't really get the benefit of anything with Tyki. They're just guaranteed a certain amount of his attention. After that, whether he helps them out or not pretty much relies on whether there's anything in it for him. Noah versions of people who were Exorcists back home don't really weird him out because he doesn't care about them either way. If they're not strong, they're boring. If they're family, they're not worth fighting and also boring. Pretty much all he CAN get out of them are the reactions. He finds a certain amusement in the ones who see everything in black and white and fight for justice or the extinguishing of ugly humanity because... well. It's never that simple.