What are some of the goals of the Red-Headed League?
The goals of the Red-Headed League seem vague. This, of course, is because such an organization does not really exist. It was invented by Jabez Wilson's assistant, who calls himself Vincent Spaulding but is really a criminal named John Clay. When Clay pretends to discover the advertisement of an opening of the Red-Headed League in the morning newspaper, he gives his red-headed employer a fallacious account of the founding of this institution at a time in the past when Wilson was apparently out of the country and could not have heard about it.
"As far as I can make out, the League was founded by an American millionaire, Ezekiah Hopkins, who was very peculiar in his ways. He was himself red-headed, and he had a great sympathy for all redheaded men; so, when he died, it was found that he had left his enormous fortune in the hands of trustees, with instructions to apply the interest to the providing of easy berths to men whose hair is of that colour."
John Clay does not say why Ezekiah Hopkins thought red-headed men needed "easy berths" more than men with any other color of hair or why Hopkins should have had "great sympathy for all redheaded men." The reader is left to assume that this American millionaire was more than a little eccentric—but at least his money was good.
Later, when Jabez Wilson meets Clay's accomplice, who calls himself Duncan Ross, it appears that one of the League's goals is supposed to be to increase the number of redheaded men in England. Duncan Ross makes Wilson believe he has been accepted to fill the vacancy but then seems to have doubts. He asks if Wilson has a family and is told that Wilson is unmarried and has no relatives.
“‘Dear me!’ he said gravely, ‘that is very serious indeed! I am sorry to hear you say that. The fund was, of course, for the propagation and spread of the red-heads as well as for their maintenance. It is exceedingly unfortunate that you should be a bachelor.'"
So, according to the man who is posing as the manager of the London branch of the totally fictitious Red-Headed League, the "goals" of the League are to encourage the propagation and spread of red-heads and also to provide for their maintenance. In other words, a red-headed man might have more children if he could afford to support them. The League will support him generously for life, so he ought to have a number of children, and hopefully most of them would have red hair.
Duncan Ross really wants to find out if Wilson has any family. He wants to feel sure that no relatives will be dropping by Wilson's shop while he and Clay are digging their tunnel. Wilson himself is too old and portly to be climbing up and down the cellar steps, but younger relatives might want to do so out of curiosity. This is the author's way of forestalling any questions in the reader's mind about the possibility of unexpected intruders discovering the tunneling.
The pawnbroker is all alone in the world. He is not very bright, as Holmes observes to Watson; so he is unlikely to see that the whole idea of "propagating and maintaining" red-heads is preposterous. His shop is ideally situated for tunneling into the nearby bank. He has plenty of free time and can easily report to the League's office every workday, including Saturday, for four hours, plus the time it takes him to get to his office and back to his shop. He is old and fat, which would preclude his ever wanted to venture down his dark cellar steps to see what his assistant is doing down there. Wilson is the ideal person for the two crooks' elaborate and audacious tunneling project. The author has created Wilson as such. He is a good example of how a fiction writer will create a character to suit the needs of the plot.