Renaming the shaders again, because the extensions I gave them were confusing GitHub's syntax highlighting.

shaders/palettePass.frag.glsl

@@ -0,0 +1,29 @@
+precision mediump float;
+#define PI 3.14159265359
+
+uniform sampler2D tex;
+uniform sampler2D bloomTex;
+uniform sampler2D palette;
+uniform float ditherMagnitude;
+uniform float time;
+uniform vec3 backgroundColor;
+varying vec2 vUV;
+
+highp float rand( const in vec2 uv, const in float t ) {
+	const highp float a = 12.9898, b = 78.233, c = 43758.5453;
+	highp float dt = dot( uv.xy, vec2( a,b ) ), sn = mod( dt, PI );
+	return fract(sin(sn) * c + t);
+}
+
+void main() {
+	vec4 brightnessRGB = texture2D( tex, vUV ) + texture2D( bloomTex, vUV );
+
+	// Combine the texture and bloom
+	float brightness = brightnessRGB.r + brightnessRGB.g + brightnessRGB.b;
+
+	// Dither: subtract a random value from the brightness
+	brightness = brightness - rand( gl_FragCoord.xy, time ) * ditherMagnitude;
+
+	// Map the brightness to a position in the palette texture
+	gl_FragColor = texture2D( palette, vec2(brightness, 0.0)) + vec4(backgroundColor, 0.0);
+}