I think it's been a while since I carried out a water-fast that was longer than 3 days. I was under the impression you were supposed to drink lots of water (approx 3 litres a day). I have been managing approx 2 litre-ish. Im not a person who gets thirsty or drink lots. In my case I have to make a conscious effort to remember to drink water, but I don't drink anything other than water generally in life outside of water-fasting.
I do remember the headache from the last time I did an extended water-fast.... incredibly bad - but not migraine like. My only slight discomfort is heartburn. As soon as I feel heartburn I drink more water.