Mystery illness

I have a friend of a friend whose cat is having some health issues that her vet hasn't been able to diagnose yet. Below is a message she sent to my friend. The tilting back of the head is unusual, has anyone out there experienced something like this?

"I am worried Gryphon isn't going to be ok.  He now won't let us touch his head and if left he just sits hunched up with his head hanging wherever he is...pic attached. I don't leave him that way but wanted to get a picture for the vet.  We pick him up gently and put him in his bed with a warm water bottle under it and he sleeps for hours.  I take him to the litter box and he uses it.  We feed and water him with the syringe.  He has diarrhea and goes back to sleep.  Starting tonight  he holds his head way back like he's looking at the ceiling but with his eyes closed and stays that way for a long time. It's so unnatural.  The vet doesn't know what it is. She is asking other vets and we are researching for hours online.  Another vet will be there to see him tomorrow, he is supposed to be very experienced with cats.  He goes back in the morning.  He has bouts of being a bit better than gets worse again."

Poor baby!  I would be scared to death.  I'm wondering if it could be an inner ear infection or something like that to make him unsteady on his feet. My other thought is that it could be something with his tummy that's making it so uncomfortable for him to move around.