I don't remember & haven't got the game installed ATM, but the kind of events you're talking about are different from the ones you could trigger via the green button right, or not?
Does clicking the green button advance time? You can only click once right?
Haven't looked at the code, but shouldn't be too hard to conjure up a mod to alleviate this pain a bit? Either cut out the RNG & let player pick an available event (or jump immediately if it's the only possible event), or be able to click the green button more than once (or both).
I think it's kinda frustrating to have a hint like "Find Erin at Lizza's 7pm-1am Saturday Night" & having a RNG involved on the background there. And if you miss it: too bad, next chance is in a week

Different wording (she
might be there), or perhaps an icon could be helpful, indicating RNG/chance is involved?
Plus, what would be neat (but perhaps that's already there?):
if you miss out, increase the chances you
do meet her next time (until it's @ ~99% / unavoidable).