Displacement works on the underlying geometry of the surface, not on any one texture layer.

It's a mistake to think of blended textures or colours as separate layers in the final render. No matter how many layers of texture you combine in a shader, there is only one surface with only one final colour value for each rendered pixel.

It sounds like you need a bump or displacement map based on the hair texture map, with the hairs as lighter strokes against a black background.

"If I were a shadow, I know I wouldn't like to be half of what I should be."
Mr Otsuka, the old black tomcat in Kafka on the Shore (Haruki Murakami)