https://bugs.mojang.com/browse/MC-4490

This is a third-person bug where the line of the fishing rod doesn't connect to the fishing rod itself when sneaking. It still appears to be present in the mod, but is less pronounced than in vanilla:

There are other issues linked to that regarding the fishing line rendering weirdly in third person that may also be fixable.

Hm there are a few mods that focus on fixing vanilla bugs like that, I think that would fit more there since this isn't adding/modifying an animation really. But worst-case could add it here.