What Might Cause Lighting Problems on Animated Mesh?

Hello, I have a lighting issue I can't seem to figure out. After going to the trouble of making 3D eyelids that open and close, I brought my character into Unity and found strange shading patches on the closed eyelids, despite having a directional light clearly aimed at them. For the sake of asking for help here, I have created a highly simplified version of what's happening, set alone in a default scene. Figures 1 through 5 show the animation progression, and in the scene view the light angle is unmistakable. Things look generally fine until Fig.4, when darkness appears where there should be light. Fig.5 shows the problem in full.

I have tinkered with every setting on the light, scene and lightmap settings, and model import settings. All normals are facing the right way, and I even tried removing the eyeball from the model on the chance that the nearness of the ball to the lid might be causing strange behavior. I've tried other things suggested in various UA topics, but nothing has helped.

Figures 1 through 5 were using the standard shader, but the problem becomes all the more pronounced with my intended toon shader, as Fig.6 shows. However, if I apply the armature modifier in Blender before import, so that the model's pose is closed by default and doesn't animate, then everything looks fine. Fig.7 shows exactly how the lighting should be hitting the model.

I am at a complete loss as to what to do about this. Any help would be greatly appreciated!