The third and last time I camped it, I was tracking it for 30+ hours (I only slept five of those 30+ hours with my character AFK at the camp in case it popped).
And yeah... it became an obsession especially after not getting a drop the first two times. I was so determined to get that drop even though the hat isn't all that great in itself. -_-
My only advice is to have a mule or second character at a weather NPC ( I used the one in Port Jeuno across from the signet NPC) and check the weather in Zi'tah every two or three hours. I never bothered camping earlier than month four in the vana'diel year nor later than month six. So while the window was a few days, rain weather isn't a constant so you can take breaks and it makes it more bearable to camp.
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