I think its just superstition. The idea is that Tae is not special at all, just a normal kid. Whereas Jaeui is a genius/prodigy. That's why there's a difference in treatment. Jaeui himself realise Tae is his lucky charm when as kids whenever Tae is sick, Jaeui will be sick. But when Jaeui is sick, Tae doesn't get sick. Also, whenever Tae feels sth is amiss or missing his brother, something bad WILL happen to Jaeui but as long as Tae is fine, Jaeui will come out of it fine. And I guess too many coincidences become "True". Also, Asian businessmen or upper class people are very superstitious. When enough people believe in it, it becomes a "fact", especially since Jaeui, a genius, believes in this. Basically if Tae died, Jaeui dies, but if Jaeui dies Tae will stay alive.
I love Passion btw but this is my main criticism of the story (novel ) . Actually the whole thing of his luck is a supernatural phenomenon, but sadly it’s not explore enough for my liking . We know is there and what it does but that’s it . However it’s one of the main reason why Tay and Ilay fit so well like it was ment to be . Ilay is the other character that because of his unnatural and inhuman nature fit that concept as well . Tay wanted an easy going life but that was never possible for him . He needed someone who will always be willing to put his life on the line for him and not die easily

Like I get Tai give his brother luck or something? But people treat it almost supernaturally while at the same time treating Tai as less than.
Honestly, it’s a really interesting concept I wish would put more focus on. Or explained better. Or I’m dumb and it’s easy to understand