It's best to divide the face into separate submeshes for the Face, Eye (pupil only), and Eyeball. This allows you to assign different material types to each region, helping eliminate unnecessary shadows in character self-shadowing.
To achieve more natural facial shadowing, enabling the Face SDF option is highly recommended. Design the lower jaw region to always cast subtle shadows, similar to how ambient occlusion maps work. When combined with self-shadowing, this can help seamlessly blend the shadows between the face and the neck, resulting in a much cleaner and more natural look.
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📺 Reference Video
The Eye shader is designed specifically for pupils and is excluded from character self-shadowing, which leads to a cleaner look overall. It also supports dedicated features like refraction and highlight effects (e.g., tear shimmer), though these require custom textures. If the eyeball and pupil are part of a single mesh, it's better to use the Face type instead of Eye.