So I picked up a manga called Kingyo Used Books. It's pretty much a manga about manga, yeah. Anyways, there's an ancillary character obsessed with an old detective series called Billy Puck by Mitsuhiro Kawashima, to the extent that he dresses like the boy detective despite being too old. But it was the
hat that caught my attention. I coincidentally picked up The Thousand Year Door on a whim, and I noticed Pennington wears the same cap:
It's not a deerstalker so it cannot be a Sherlock Holmes reference. And It doesn't evoke any other influential detective series that I'm familiar with.
There is unfortunately almost no English or Japanese sites dedicated to Billy Puck.
Yahoo site is the only page I've found regarding Puck or his creator. But I'm not about to doubt that such a property has a strong cult following there.