Now for the fringe theory. Ilima is probably based in or around the city due to his attire.
The official bird of Honolulu is called the fairy tern. They're pretty proud of it because for some reason the seabird nests in large numbers only on remote islands and the capital city. Ilima is also a lei plant, albeit there are actually a shit ton of lei plants so comfey.
You should also be greeted with a lei when you arrive, so if the stereotypes add up, he could be fairy. Also is think that Gumshoos was at around second gym leader levels, so that's a thing.
video I guess
https://youtu.be/RdDkatpLDNo 