I haven't looked at Alicorn's data, but when I get a headache my first two hypotheses are that its caused by either dehydration or caffeine withdrawal. Either I drink something caffeinated or drink about 16-24 fluid ounces of water and then re-assess after about 20 minutes. If whichever I tried doesn't work then I do the other thing plus take a pain killer (choosing between aspirin, acetaminophen, or ibuprofen based on other considerations) because by that point I just want the problem to go away rather than to gain a bit of information about which particular solution fixed things. Usually, my first experiment works and no pain pill is required.

Caffeine is a diuretic (meaning it makes you pee) meaning you have to drink more than otherwise in the long run to balance this effect.

Something potentially worth noting if you're drinking a lot of green tea is that its cancer preventing effects appear to follow a dose response curve that has been experimentally observed up to six or seven cups a day, so drinking a lot of it can be worthwhile if that's important to you. Green tea's cancer-protecting mechanism is probably a body-wide up-regulation of apoptosis (programmed cell death) killing potentially cancerous cells earlier than otherwise. One minor worry with this (that I've never seen addressed in the literature which is more of an untrustworthy pet theory of mine) is that apoptosis up-regulation can presumably cause more neurons to die and apoptosis inhibiting mutations like BRCA1 have been suggested as leading to higher IQ. My guess is that there may be a trade-off here between raw biological longevity and high fluid intelligence.