2D Lighting Rotation Confusion

I'm trying to add some basic 2D lighting to a scene in Unity. I've got a material with the standard material, a texture and a normal map. As a test, a set the whole normal map to RGB (127, 127, 255), which tutorials have defined as the neutral normal, indicating a surface facing the camera.

When I put my material on a Sprite and add a directional light, I get an odd result. When the light faces the sprite (0, 0, 0), it's hardly lit at all. When the light faces left (0, 270), the sprite is fully lit, and when it faces anything from y=[1-179] the sprite isn't lit at all. Essentially, it's as if the light is rotated 90 degrees to the right of reality at all times.

Did I fundamentally misunderstand something about normal maps (maybe confused the coordinates)? Or am I doing something wrong in Unity? Any help would be appreciated!