How I think each of the ghostbusters would get Egon to go to bed when he's overworking himself and on his 18th all-nighter of that week
Egon's awful at taking care of himself and his sleep schedule but Ray is also awful at it and is only just marginally better. 7 times out of 10 Ray's there with Egon during these all-nighters, but he's just slightly smarter enough to realize that he needs sleep at one point.
That being said when he recognizes it's not just time for him to sleep but Egon as well I feel like his method would be to tire him out. Because he's the closest to Egon he'd have the best chance at convincing him, but he knows best how stubborn Egon is and realizes trying is futile.
He might try to convince him at first even if he knows it likely won't work just to get the thought in Egon's head, then work alongside him until he's sure Egon's tired enough to not argue (impossible, unless it's Ray) and then usher him off to bed. While this method comes at the cost of his own sleep it's not like it's something he hasn't gone through before
Peter makes a comment early in the game at the Sedgewick level how Egon gets cranky when he hasn’t had a nap (same game where Egon admits to only sleeping for 14 minutes a day) so I feel like Peter would only really step up when it starts to affect Egon’s mood and such.
That’s not to say he only cares about Egon taking care of himself when it becomes an inconvenience he can notice but for Peter it’s three things.
1) Egon’s a grown adult who can take care of himself even though he chooses not to.
2) Peter himself doesn’t always make the smartest or healthiest choices, so while he’ll judge regardless on if it’s his place to do so or not there’s no point in policing him when he has his own faults and when, if he’s being honest, Egon seems to make it work. If anyone else tried what Peter has he’s sure they’d have lost their mind by now.
3) this is the most important one: Egon is a stubborn ass. Peter’s persuasiveness and Egon’s stubbornness are like if an unstoppable force and an immovable object collided.
The only times Peter would get riled up in an argument are if it happens in high stress situations, after a long/bad day, or with Peck. Otherwise he’s usually the one to rile up others. Egon’s not totally immune to this but somehow—in a way that shouldn’t be possible for a man as unsociable and introverted as him—he’s found a way to push Peter’s buttons as well. It’s something that’ll only happen in the above situations such as if they’re under high stress or having a bad day but it’s happened enough times for Peter to put off arguing with Egon about petty things and handle it in ways that are more successful in the face of his stubbornness.
The first would be pestering, which is totally different from arguing because it makes you immune to getting ragebaited. Definitely. He’d likely just pester Egon by blabbing on about his day, asking Egon a ton of questions they both know he doesn’t care to hear the answers for, or messing with little things around the lab he sees that he’s 89% sure won’t explode if he touches them until it annoys Egon enough into realizing the only way to avoid Venkman is through sleep.
The second would be bribery. Leaving him candies or sweets or promises of them if he hauls his ass to bed for one night. Like Santa for people who need to take remedial classes in how to take care of yourself and make sure you don’t pass out or die.
I feel like Winston is secretly Egon’s favorite. He’s competent, easy to get along with, smart in ways the rest of them aren’t which helps make up their team composition and honestly a breath of fresh air.
Now it would depend how long he’s been with them when trying to get Egon to go to bed but I feel like he’d be lest pestering or forceful than the others both because that’s just how he is but also maybe a small lingering feeling he’s not as close with the rest as he could be since he wasn’t there for their college days. It’s not a feeling that controls him or keeps him up at night but is more of a slight reminder when seeing them interact and such. Rest assured though he’s as equally important as the rest are to this found family that was found in a dumpster.
Winston’s method would probably involve him trying to convince him—which I lied earlier I think Winston would have the best chances of convincing Egon to go to bed through conversation—and when that fails and he realizes Egon’s not going to sleep any time soon might stay with him a little longer.
He’d probably use this chance to have more 1 on 1 conversations with him since they hardly get the chance (seriously I don’t think they have any solo interactions in the movies) and ask him about what he’s working on. Egon would have to take more time explaining it since if Ray were to ask it’d be something he’d likely already know or could catch on quick too and with Peter he’d stop listening halfway in.
Something else I think Egon would enjoy about Winston are his listening skills. It’s really fun to talk to someone about your work or passion or interests that they have no knowledge in since you get to explain a lot more, especially when that person is showing genuine interest regardless if they’ll truly grasp it or not and, in Egon’s case since ladies crush on him the most in canon (RGB at least), aren’t just letting him ramble on because they find it “hot” without any intent to absorb any information.
I think eventually the enjoyable conversation would relax Egon enough into being too tired to continue working, and so he’d accept defeat and pick up where he left off in the morning (whether this is something Winston realized and does intentionally or is something that just happens because he’s goated like that is up to you)
Later on though, when he’s more comfortable with the team and has been with them awhile he’ll definitely resort to stealing Egon’s candy/junk food stash if he has to. Egon can be mad at that all he wants but can’t do anything with his mind all sluggish from the sugar crash
This characterization is closer to her RGB counterpart but that’s because RGB Janine is the goat and movie Janine has like 13 mins of screen time and idk what to do with that lol
But I feel like her method would be pestering, or rather nagging, much similar to how Venkman does it. Just lecturing him on how bad what he’s doing to his health is until eventually it wears him out or she makes an argument that his mind, stubborn as it is, can agree with.
That and going more along with RGB characterization I feel like he’d have a soft spot for her and wouldn’t want her to worry that badly
Anyways I should practice what I preach since I’m writing this at 1am goodnight!!!