Ah well in the post before that I mentioned the Immortal old man with an enormous mustache, he has even appeared in IC already.
But yeah, not Igor. If it was Igor I would have just typed Igor.
This old man is very manipulative, he would have to be to survive politics in the nexus, and he has been alive for a very long time even by the standards of immortals.
Anyway you are right for the most part, Minato basically does just wander aimlessly at night having random encounters unless someone comes to him with a request. Usually the requests end up being to kill something or other so same old same old for him either way.
Plus over the course of years he has to have fought, and killed, a number of fairly bad things through simple odds of encounter, you have to think, what might he have run into over the course of three years?
I will mention again that Minato did not actually play much of an active role in the development of this setup, it was that scheming old man.
I am sorry if this doesn't make much sense, if it makes it easier the district could be an out of the way section far away from most of the conflict centers, and in a less urban part of the city. I had sort of thought of it that way already anyway.
Smaller buildings, small businesses, residential spaces that sort of thing.