I think if sick, Bill would either make a full on production out of it ('i am LITERALLY dying) and be super whiny and pathetic about it.
Or he'd be stupid about it and refuse to say shit because he is allergic to showing any sort of vulnerability. So he's just even more of an asshole and nobody can figure out why. And if anyone picks up on the fact that his dumbass is sick, he doubles down on the denial. If you somehow bully him into resting? Immediate switch to whiny and pathetic.
Either way he's annoying while sick and you end up wanting to throw him out of a window for being a stubborn asshole.
See, that's how I envision it too!
Obviously, of all the members, Jerry would be the most 'normal' whenever he's sick, as he would protect himself and others (distance himself, wear a mask, etc.). If he feels too ill to attend a meeting, then he simply wouldn't go. But alas, he would show up regardless due to the club's (Bill's) beck and call. Pete doesn't give a single fuck about being sick, and 99% of the time, he powers through it; you think a little bit of phlegm is going to stop him, ha, good luck, buddy. He has seen worse things than a scratchy throat, running nose, and pink eye in '80s b-horror films ALONE.
As for Josh, I think he would lean more towards the pathetic side. He'd complain about not wanting to leave the comforts of his room, more particularly his bed. Either you bring the club to his doorstep, through videocall or quite literally, or he's not attending. At all. Which, honestly, I think Bill would be rather pleased about this outcome.
Even if he DOES attend, he believes he shouldn't lift one of his grubby little fingers or raise his voice, for that matter. He has to conserve energy after all, he wants to get over this illness before the theatre shows Return of the Jedi.
Now, for Bill, he's 50/50. I love the idea that he's just an insufferable bastard whenever he's sick, and it's an unspoken rule amongst his 'friends' to never bring it up, as it's just going to make matters a fuck ton worse. "Oh, just because I'm sick, you thought we weren't going to have a meeting? Better yet, you thought someone was going to temporarily step in for the President's position? Nice try, jackass!"
Perhaps he'd even use his running nose and occasional sneeze for pity points. Maybe each of the other members has to scramble and bring him a gift before their next meeting? Oh, and it BETTER be a good one. If you get him nothing, or better yet, something worthless in his eyes, he equates it to you wishing death upon him.
However, deep down, I believe that perhaps one of the reasons why he's whiny and childish whenever he's sick is that he yearns for the feeling of being comforted(?) Sure, he puts up this front of being a stubborn asshole, denying that he's ever sick; meanwhile, he's running a 101 fever, but do you know how long it's been since his mother, or perhaps both parents, took care of him?
Like, genuinely showing concern for him, making sure he's comfortable and attending to his needs, rather than having his mom tell him there are pills in the medicine cabinet and to sleep it off?