Oops! This is embarrassing
We don't have much data for Fair Skies right now, if you have some to share please post a comment for others kupo!
Located at the "Habisphere" fishing hole in Azys Lla, x40, y18.
Time of Day: Any
Weather: http://xivdb.com/weather/2/fair+skies → http://xivdb.com/weather/9/thunder
http://xivdb.com/action/4105/fish+eyes: Yes. 3 minutes.
Folklore Book: http://xivdb.com/item/12703/tome+of+ichthyological+folklore+-+abalathia's+spine
Caught with 801 Gathering, 640 Perception.
Mind the weather transition. You will also need to use Fish Eyes. It's a fairly generous 3-minute buff. You will first have to mooch a http://xivdb.com/item/12805/rudderfish, which has a medium tug with a 13~15 second cast time. The Crystal Pigeon will be a big fish tug, and it doesn't take too long to bite.