There is a short answer and a long answer to this question.
The league was ostensibly a society established by an eccentric rich man that benefited red-headed men by employing them. The league hired Jabez Wilson to come to its office and do bizarrely minor clerical work: spend the hours of 10-2 copying pages from Encyclopedia Britannica. Jabez spent seven weeks writing before he was informed that his services were no longer needed, because the league had ceased to function.
The long version is that Wilson's actual function for the "league" was dupe. The league did not exist, although someone did rent an office and he did go there and copy the book. Wilson had a real job, or rather business, that of pawnbroker. It was this business, especially its location, that made him useful to the people who invented the deception. They were paying him to be away from his shop so they could get up to no good there.