hi--Very occasionally I wake early in the morning with a really, really bad headache, but I can't recall being awoken in the middle of the night. I am an insomniac and take a sleeping pill so perhaps I am in pain but sleep through it. When I do wake in the morning with a migraine it's always at a very high pain level, so perhaps I sleep through the beginning and middle pain levels.
When I first noticed pain coming on at the same time every day, it would start at 3pm, and that was consistent for a couple of years. I've also had periods of time when they started at 5pm, 6pm, and right now they start 10pm-midnight. I can have headaches at other times of the day.
The other odd thing I've noticed: whenever I get sick, like with a flu or GI or Lyme flare-ups, my headaches stop for the period of time I'm sick. They restart after I've recovered. I think that's odd, but maybe other people have this?