Is it common or normal for Alzheimer's patients to pull out their hair?

As my dad progressed in his dementia, and mom continues to, they each became more and more focused on whatever may have been a minor obsession before dementia. My parents were both always anxious people before dementia, and they used various behaviors to soothe those anxieties. Dementia magnified those behaviors beyond anything I might have guessed. Ultimately mom had to be put on some resperidone to keep some of her behaviors in check. She is by no means “zombied out” by the meds, just slightly less involved in those behaviors. You mention that your dad is in the end stages. My parents have been on palliative care only, since last May, and dad passed last November. We stopped all specialists last May too. I knew they neither one wanted the life they were living, and so as long as they were/are kept comfortable, we are not treating illnesses, only uncomfortable symptoms. Everyone’s situation is different and I would never presume to tell you what you should do. This is just how our family has handled our situation. I hope it is somewhat helpful. Your dad is blessed to be so loved.

Hair pulling is a known addiction. I knew one girl who was doing this and was practically bald before she sought help. It is strange, but real. I don't know how it may apply to Alzheimer's.

I would ask if anxiety meds would help. My Mom started to hum and it got louder each day. The gave her something to calm her.

Regarding the squinting, is it possible the light is simply too bright for him? Perhaps he has become excessively sensitive to what would otherwise be considered ordinary illumination.

You may want to look up "Trichotillomania" as a diagnosis.
And check to see if Dad is also eating his hair.

He could be anxious.

I wonder if it’s part of the “fidgets”. Advanced Alzheimer’s patients I’ve seen often picking at their clothes, their skin, anywhere they can. His hair maybe the only thing in his reach. He may draw some comfort from it, in some odd way.