The bug

The way in which the anvil texture is mapped to the model is very strange and does not appear to follow any expected pattern, making it difficult to develop textures for this block.

How to reproduce

A debug resource pack is attached to this ticket so you can check how the mapping works.

How to fix

A fixed version of the anvil template model is attached that changes the mapping to the would-be defaults, improving the look. This issue can be fixed by replacing vanilla's anvil template model with this.