Someone pointed out that the fishing abilities (mostly traits) are listed on xivdb.com
Here's a version I did myself. Wondering if Rein or anyone else would like to cross reference or correct
CAST Commence fishing. Obtained Fisher Lv.1 Requires FSH
EXIT Cancel fishing (and return to normal mode.) Obtained Fisher Lv.1 Requires FSH
TN: Everything from this point on are traits.
DISCOVER SPOT Locate special fishing spots up to level 35 and become able to fish there. Obtained Fisher Lv.15
ENHANCED STEALTH Increases the range of enemies avoidable when using Stealth to level 30. Obtained Fisher Lv.18
(TN: I assume you learn STEALTH at level 8 like the other gathering classes).
ENHANCED STEALTH II Increases the range of enemies avoidable when using Stealth to level 40. Obtained Fisher Lv.28
DISCOVER SPOT II Locate special fishing spots up to level 44 and become able to fish there. Obtained Fisher Lv.33
SAND FISHING Become able to cast in sandy soil. Obtained Fisher Lv.35
ENHANCED STEALTH III Increases the range of enemies avoidable when using Stealth to level 50. Obtained Fisher Lv.38
SET FREE II Set a caught fish free to use as bait. Obtained Fisher Lv.40 (TN: Seems this is a trait, not sure what the ability does before this level or at level you learn the actual ability).
DISCOVER SPOT III Locate special fishing spots up to level 50 and become able to fish there. Obtained Fisher Lv.43
CLOUD FISHING Become able to cast in a sea of clouds. Obtained Fisher Lv.45