I did jarthur shared body hcs awhile ago but I've been reading a lot of fics of them post s6 with separate bodies so here's some random jarthur separate bodies hcs for your enjoyment:
They are so used to sharing a body that once separated, things like privacy and personal space don't really occur to them as something they should pay attention to with each other. It is very common to see them taking up the same physical space (brushing up against each other, leaning full chest-to-back over each other to look at something, physically moving the other instead of asking them to move, etc., etc.), and they are almost always touching in some way. Their default standing positioning in almost any situation is John slightly behind Arthur, with their shoulders pressed together. If one of them is seated, the other is probably either hovering behind them or perched on the arm of their chair. They do not find their physical proximity to be strange in any way because they've been a lot closer. They don't even notice how close they are unless someone else points it out, which isn't very often since people think they're freaky, so they try not to draw their attention.
Arthur is a decently tall man, but John is a good half foot taller than Arthur, and a bit broader. The sudden height difference is a bit of an adjustment for John, as he had become used to seeing things from Arthur's height and judging distances in proportion to Arthur's body size, so he bumped into a lot of things in the first few days of walking around in his own body.
Because they primarily interact with each other, John is less aware of the social norms of personal space than most people are, and therefore, has made multiple people uncomfortable by getting too close to them/touching them to move them out of his way. Arthur is subconsciously aware of John at all times, so he will subtly pull John back to his side if he's getting too close to other people and make apologies if necessary. The only other person who doesn't seem to mind John's extreme closeness is Faroe because she recognized very quickly that physical proximity to someone he knows seems to be a sort of comfort for John, so she made an effort to be close to him, and now she doesn't think anything of it. She pretty frequently leans on him and links arms with him when they’re walking, particularly if Arthur isn’t with them, because she wants John to feel comfortable.
Despite his earlier complaints that Arthur could talk to anyone, while he was only able to talk to Arthur, John doesn't actually have much of a desire to speak to other people very often. He is fully capable and does not have any anxiety about talking to other people; he just doesn't really want to. Most of the time—whether it's as simple as ordering something at a cafe or as complex as communicating with police about a case—Arthur is the designated talker of the two of them. It's not uncommon to see John lean down and say something to Arthur while he's talking to someone else, and have his input voiced by Arthur instead of just outright saying it. John's a bit of an attack dog, though, and he loves a good argument, so he is more than willing to yell at someone, particularly if they are brushing off, ignoring, or being rude to Arthur. If a point needs to be made, John will make it, and since he is more physically imposing and doesn't speak as often, people tend to listen to him. However, John does occasionally forget that other people can hear him now, and he has openly insulted multiple people while standing right in front of them.
If their investigations require touching any unknown or gross-looking substance, it automatically becomes Arthur's job because John will refuse. The idea that if Arthur has not touched it and deemed it acceptable, John will not touch it applies to most things, even if they are just regular objects that he has not seen before, because he is very picky about the texture of things that he touches. The only exception to the rule is corpses because he has to touch them for his visions to work, but he hates doing it. There have been multiple instances of people attempting to hand him things, only to have him stare at them until Arthur reaches around him and grabs the thing, but if Arthur hands something off, he won’t bat an eye before taking it. He also avoids shaking hands with people as often as possible, usually by either busying himself with something else or simply hanging back from the conversation, because he doesn’t like not knowing what their hand is going to feel like before he touches it.
Arthur had a hell of a time introducing John to food because he is also a very picky eater. They discovered that John hates anything bitter or sour, but he is weirdly into spicy food. The first thing aside from water that John ever consumed was a sip of Arthur's coffee, which he promptly spit out and declared disgusting. John prefers tea, but if he has to drink coffee for whatever reason, he takes it with honey and a bunch of cream, which Arthur finds horrifying and much too sweet. They are chronic meal repeaters because John is very hesitant to try new things.
John will occasionally catch himself describing things to Arthur and apologize, but Arthur always tells him to continue, even if he's actively looking at the same thing, because he likes the way John seems to find beauty in the most mundane things. Even when John isn't around, Arthur finds himself taking more time to just take in the world around him than he ever has before, wondering what John would think of certain sights. If John is around, he will sometimes prompt him to talk about what he's seeing just because he misses the way John describes things.