Now that I think about it, I don’t think acetaminophen has been effective in ever curing my headaches even back when I was prescribed liver damage amounts.

Sleep apparently > painkillers

I wouldn't necessarily generalize; even if acetaminophen doesn't work, other painkillers like aspirin or naproxen sodium might. (Personally, I take naproxen sodium and only naproxen sodium when I have a headache.)