How to make parts of a texture to be always lit?

I have a simple 2d character, and I want to make its eyes (flat black and white) always visible, no matter the lighting in the scene, (like 2d cartoon show characters, where the eyes are always visible, even in complete darkness). I have assigned the Sprites/Diffuse material to the sprite, and it works just fine with my light settings. However, I cant figure a way to assign a different shader to the eyes (maybe using an alpha map, like I usually do in Blender to mix shaders). I tought I coud use a custom shader, that makes the pixels of the eyes ignore light, but had no luck.

Another option would be to use different sprites for the eyes, and link them to the body, but then, I would have to sync everything manually.

You can always use a material with emissive map, which would make the eyes lit no matter what lighting conditions you have.