Falling Asleep on Lookism Men
I might do a part 2 if this is well-received. Sorry if OOC, I've never written a fanfic before, but I worked up the courage!!
Reader falling asleep on lookism men, cuddling talk, genderless terms and no physical traits of reader mentioned.
Includes: Gun, Kitae, Jake, Samuel
Gun:
Overall, I can't see Gun greatly inconveniencing himself for the reader, like refusing to move or putting off his day just to avoid waking them. If he does have to leave, he'd make sure the reader is comfortable before he goes, a loving gesture in his own way. Gun doesn't want them falling asleep in an awkward position and possibly hurting themselves.
I don't imagine Gun to be a "natural" cuddler type, but for you, he'd tolerate it and do his best not to disturb you with too much movement. On days when he isn't busy, he'd stay as still as he can without completely inconveniencing himself.
Over time, I think Gun would come to genuinely enjoy the peace and security of the reader choosing to sleep on him. Listening to your steady, rhythmic breaths would put him at ease. I especially think he'd like it when the reader falls asleep on him while he's occupied with his hobbies, which seem pretty quiet and peaceful, like woodcarving.
Kitae
Kitae doesn't seem to mind people (or at least the ones he "likes") falling asleep or resting on him. If anything, he seems to enjoy lounging around himself quite a bit. (Though I can't actually tell if Kitae ever sleeps,, maybe that would explain the dark circles.)
I think Kitae would be more than fine with the reader falling asleep on him, so long as they're not getting in the way when he's handling business that has him constantly getting up and moving around. If it's a long meeting, I think he'd have no issue with the reader cozying up against him. Who in their right mind is going to make a comment about you? If you're at home, I think he'd be pretty indifferent about it too. He isn't going to go out of his way to make you more comfortable, but he won't move you either. I don't imagine he sees much intimacy in it; if it's something you enjoy, it doesn't bother him. He might even take the opportunity to catch some sleep himself.
If he doesn't have the time to let the reader sleep on him, I think he'd be pretty callous about moving you off. I don't imagine he'd be especially rough or violent (at least not on purpose), but he wouldn't bother setting you down somewhere cozy either. He feels no guilt about acting in his own interest, and if he has somewhere to be, that's his priority.
Jake
Jake would be thrilled if he has nothing to do and a sad if he's busy and has places to be.
I can see Jake being a big cuddler. I think it would be a huge source of pride for him that the reader feels safe and secure enough to fall asleep on him, and because he doesn't want to break that trust, he'd struggle to move unless it's genuinely urgent. He's a boss, of course, so if push comes to shove, he'll carefully move you somewhere cozy and come back as quickly as possible so the reader knows they weren't abandoned.
If it happens during the day, I think it'd stress him out a bit more. Big Deal needs him constantly, and he struggles to find a balance between his responsibilities and the people he loves, something his father struggled with, too, which might make him anxious about the situation, even if it is just moving you as you sleep.
I think Jake would love it most if the reader chose to curl up with him at night or in the evening, when everything has finally settled down. Then he can give the reader his undivided attention and soothe his own worries by listening to the steady beat of your heart. It's in moments like those that he feels the safest and most at peace. More than anything, he hopes the reader understands that even though he's busy being a boss, he'll always do whatever he can to make time for them, and he feels genuinely honored that they trust him enough to fall asleep on him.
Samuel
I think Samuel would behave a lot like Kitae, though less callous. It would definitely annoy him if the reader fell asleep on him while he's busy. He's constantly working and would probably think, "Couldn't you just sleep at home or at night?" If the timing is especially inconvenient or unprofessional, I could even see him waking the reader up. (not in an aggressive way)
If it's a situation where he can stay seated, though, I think it might fuel his ego a bit to have somebody beautiful resting against him. At the same time, I don't think he'd like other people paying too much attention to you while you sleep, and it might make him a little jealous or irritated.
At home, it's kind of hard for me to say whether it would annoy him or not. He seems to value his personal space quite a bit. I don't think he'd resent the situation or the reader of course, he just wouldn't really understand it. If the reader explained that falling asleep on him makes them feel safe and comfortable, I can see him becoming much more tolerant of it. Maybe it would even make him happy that somebody sees him as a safety net. It might make him feel strong or chosen in a way. He'd definitely prefer the reader keep it as a home activity, though, where he can still do his own thing while keeping the reader comfortable.