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 hasnβt 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 Egonβs mood and such.
Thatβs not to say he only cares about Egon taking care of himself when it becomes an inconvenience he can notice but for Peter itβs three things.
1) Egonβs a grown adult who can take care of himself even though he chooses not to.
2) Peter himself doesnβt always make the smartest or healthiest choices, so while heβll judge regardless on if itβs his place to do so or not thereβs no point in policing him when he has his own faults and when, if heβs being honest, Egon seems to make it work. If anyone else tried what Peter has heβs sure theyβd have lost their mind by now.
3) this is the most important one: Egon is a stubborn ass. Peterβs persuasiveness and Egonβs 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 heβs usually the one to rile up others. Egonβs not totally immune to this but somehowβin a way that shouldnβt be possible for a man as unsociable and introverted as himβheβs found a way to push Peterβs buttons as well. Itβs something thatβll only happen in the above situations such as if theyβre under high stress or having a bad day but itβs 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. Heβd likely just pester Egon by blabbing on about his day, asking Egon a ton of questions they both know he doesnβt care to hear the answers for, or messing with little things around the lab he sees that heβs 89% sure wonβt 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 donβt pass out or die.
I feel like Winston is secretly Egonβs favorite. Heβs competent, easy to get along with, smart in ways the rest of them arenβt which helps make up their team composition and honestly a breath of fresh air.
Now it would depend how long heβs been with them when trying to get Egon to go to bed but I feel like heβd be lest pestering or forceful than the others both because thatβs just how he is but also maybe a small lingering feeling heβs not as close with the rest as he could be since he wasnβt there for their college days. Itβs 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 heβs as equally important as the rest are to this found family that was found in a dumpster.
Winstonβs method would probably involve him trying to convince himβwhich I lied earlier I think Winston would have the best chances of convincing Egon to go to bed through conversationβand when that fails and he realizes Egonβs not going to sleep any time soon might stay with him a little longer.
Heβd probably use this chance to have more 1 on 1 conversations with him since they hardly get the chance (seriously I donβt think they have any solo interactions in the movies) and ask him about what heβs working on. Egon would have to take more time explaining it since if Ray were to ask itβd be something heβd likely already know or could catch on quick too and with Peter heβd stop listening halfway in.
Something else I think Egon would enjoy about Winston are his listening skills. Itβs 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 theyβll truly grasp it or not and, in Egonβs case since ladies crush on him the most in canon (RGB at least), arenβt just letting him ramble on because they find it βhotβ 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 heβd 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 heβs goated like that is up to you)
Later on though, when heβs more comfortable with the team and has been with them awhile heβll definitely resort to stealing Egonβs candy/junk food stash if he has to. Egon can be mad at that all he wants but canβt do anything with his mind all sluggish from the sugar crash
This characterization is closer to her RGB counterpart but thatβs 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 heβs 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 heβd have a soft spot for her and wouldnβt want her to worry that badly
Anyways I should practice what I preach since Iβm writing this at 1am goodnight!!!