Oral chemo doesn't normally kill head and neck cancer. If your father is in good health surgery is an option, normally.
I'm not quite sure what is going on with him. Based on your description, it sounds like he had a recurrence (which this close to radiation sounds more like they never got it all to begin with) I would be very surprised if the chemo killed it (maybe the dr missed seeing the tumor?) did they do just a PET and determine the cancer was back and treat him with the oral chemo? Or did they actually biopsy the area? It could be if they didn't do a biopsy that it wasn't even cancer.... And that is why the chemo worked. Now it may be... Have they confirmed that this free roaming cancer is really cancer?
Are you at a top medical facility?
Best of luck