Yours is not the best way to do it, although it's theoretically possible. The proper way would be to set the light to be a child of the camera (which should in turn be a child of the whole fps controller thing) and make it face the same way in edit mode. Then, when the camera rotates, the light will rotate with it. This will make the light follow every movement of the camera without delay.

You can just make the directional light a child of the first person controller, then it will follow it around in the direction that you are facing on the x and z axis. However if you want the light to follow the mouse in other planes then you'll need to write a function.

Thanks I thought there would be a simpler way to do this. The only problem is if I add the light to the built in FPS Prefab it breaks it. I presume to do this I will need to create a new FPS prefab with the light included.