Is Billy Puck the name of the ancillary character in question or the name of the detective series he's obsessed with?
I assumed my last lines made it clear that it is the latter (Though, the character in question does
go by Billy as a nickname). On that note, Google translate borked up my link. Here's the Yahoo page I meant to link to.
On the topic of if it was a reference, I kinda doubt it. They look similar, but, aside from not being a deerstalker, they also look similar to the famous SH deerstalker. I mean, how many people do you know call it a deerstalker and not a SH hat? Maybe the fact that it's plaid and British-... ish is supposed to evoke a Sherlock Holmes feel.
'Cause people, whether or not they know it's called a deerstalker, know what it looks like without even needing a reference -- two brims and two earflaps (invariably tied at the top). You cannot mess it up even if you're only passingly familiar with SH. It may be that Kawashima intended to evoke SH, but that's not really the point. PM2 gave a character -- a detective wannabe -- a distinctive article (i.e., exact type) of clothing iconic as a cult detective character. For what purpose would they give it to Pennington other than signify his hobby vis-a-vi an establish detective?
FTR, Puck is half-American, half-Japanese (I cannot recall on which matrilineal/patrilineal sides those fall on).