Here's an animated eyeball (hat tip chatgpt):

    uniform float time;
    varying vec2 vUv;
    vec3 lighting(vec3 normal, vec3 eyeDirection, vec3 lightDirection) {
    float diffuse = max(dot(normal, lightDirection), 0.0);
    vec3 reflected = reflect(-lightDirection, normal);
    float specular = pow(max(dot(reflected, eyeDirection), 0.0), 16.0);
    return vec3(0.1) + diffuse * vec3(0.5) + specular * vec3(0.3);
    }
    void main() {
    float theta = vUv.x * 2.0 * 3.14159265359;
    float phi = (1.0 - vUv.y) * 3.14159265359;
    vec3 sphereCoord = vec3(sin(phi) * cos(theta), cos(phi), sin(phi) * sin(theta));
    vec2 irisPosition = vec2(sin(time * 0.5) * 0.1, cos(time * 0.7) * 0.1);
    float irisDistance = length(sphereCoord.xy - irisPosition);
    float irisRadius = 0.25;
    float pupilRadius = 0.1;
    float irisEdgeSoftness = 0.02;
    vec3 color;
    if (irisDistance < pupilRadius) {
        color = vec3(0.0);
    } else if (irisDistance < irisRadius) {
        float t = smoothstep(irisRadius - irisEdgeSoftness, irisRadius, irisDistance);
        color = mix(vec3(0.0, 0.0, 1.0), vec3(0.5, 0.25, 0.0), t);
        color += 0.05 * sin(20.0 * irisDistance + time);
    } else {
        color = vec3(1.0);
    }
    vec3 eyelidColor = vec3(1.4, 0.90, 0.60);
    float blinkSpeed = 0.5; // Reduce this value to slow down the blinking
    float blink = abs(sin(time * 3.14159265359 * blinkSpeed));
    float eyelidPosition = mix(0.4, 0.5, blink);
    float upperEyelid = step(eyelidPosition, vUv.y);
    float lowerEyelid = step(eyelidPosition, 1.0 - vUv.y);
    color = mix(color, eyelidColor, 1.0 - upperEyelid * lowerEyelid);
    vec3 normal = normalize(sphereCoord);
    vec3 lightDirection = normalize(vec3(0.0, 1.0, 1.0));
    vec3 eyeDirection = normalize(vec3(0.0, 0.0, 1.0));
    vec3 litColor = color * lighting(normal, eyeDirection, lightDirection);
    gl_FragColor = vec4(litColor, 1.0);
    }