AD&D 1e actually has pretty in depth rules for finding henchmen. Players generally aren’t very happy with it, since it costs 100s of gold and in-game weeks to find random lvl 1 NPCs with no equipment. Like all of 1e’s rules, it’s pretty punitive on the players seeking henchmen. This can be justified, as henchmen properly run are a huge boon to the party, and it prevents the henchman from becoming disposable.
I don’t think I’ve ever been in a game where the DM used these rules as written.
My favorite way of introducing henchmen to the party is for them to persuade or subdue NPCs our in the wild to join them.