In my country, Chile, we have a lot of weird idioms and slangs, here the word "Pico" is used as "dick", pico is also the beak of the birds, so that's where the relationship comes from.
Aaand, here we usually said the phrase "the pico day"/"el día del pico" (the "dick" day) when someone try to said that something will never, ever, happen, because between jokes, there will never be a "day" of celebration for the penis.
It is said in super informal language, so i could say something like "the day of the dick i'm going to pay you the money" ("el día del pico te voy a pagar la deuda") to say that he will "never" pay you a debt, in a somewhat insulting way. Also you can said something like "suck my dick" like "chúpame el pico" (suck my "pico")
Thats why this is so funny for me lol.
You can also imagine that many people in our country commented back in the days that, product of globalization and things like the Internet, we learned that, indeed, there is a "penis day", which is celebrated in a town in Japan.