When attempting tp create a GI effect on shag hair (hairFX), you can convincingly fake it. Heres how I do it:
For the head hair, you can create a mini “sky light dome” for the head by linking four target spot lights to the head of the rig. One pointing towards each ear, one behind and above and one in front and above. These are pretty close to the head, about a “head” away. These only light the shag hair, all else is excluded from these light’s illuminations. Only the two lights above cast hair shadows.
You can fake/enhance the hairline and underlying shadows on the head by creating a non-renderable “bonnet”. It should be linked to the skull and have a semi transparent material on it that you can adjust the transparency of. Use it to cast shading on the part of the head that is “under” the hair and at the hairline. This can be extremely convincing.
If you are animating the character, you could link the “4 light dome” to a dummy that is linked to the head, but uses constraints to remain aligned to the world space. This way the dome “follows” the head, stays centered about it, but does not rotate with it. So when the head rotates, the highlights on the hair realistically change.
Finally, if you are using IBL, you can even use your hdr in the specular color of your hair shader, this will help to create even a more convincing illusion of GI on the hair.
Good luck!