Comments by Date (2)
If it's anything like the Summer Bass/Winter Squid, then "summer" starts in March around the Vernal Equinox and continues to the Autumnal Equinox in September. You can always catch one or the other of those fish; there's never a time when neither is available.
Tailors have a chance whenever making Imperial Silk to get this or the Imperial Silkworm. So while they are produced by tailoring, there is no pattern to learn(aside from Imperial Silk and Song of Harmony) and you can't produce them on demand. The items are BoE, so after you get your personal pets, time to profit.