The whole keto stick thing is bullshit IMO. Think about it, the sticks measure the concentration of ketones in the urine. Now, if you are drinking a lot of water/lquids your urine will be dilute. Soooo dilute urine = less concentration of ketones.
Those who mention headaches during ketogenic diets are usually experiencing them as a result of lack of hydration. I am sure many will say "I drank a ton of water", and that may be so, but that is typically the reason. Here is a nice explanation :
Serotonin seems to have a central role in headache pain (nociception). Migraines are linked to too little serotonin activity resulting in vasodilation and tension headaches are linked to too much serotonin activity resulting in vasoconstriction. Abnormalities in magnesium or calcium availability also tend to adversely affect blood vessels in the brain ability to contract and dilate appropriately.
Going on any variant of low-carb dieting causes serotonin activity to drop off because of how the how the blood-brain barrier works and the decreased availability of the amino acid tryptophan. When blood sugar goes up, insulin is released which causes most other amino-acids to be taken up from the blood stream by muscle tissue, but not tryptophan (reference). The resulting high ratio of tryptophan in the blood stream allows it to cross the blood-brain barrier preferentially which makes it more available to be converted to serotonin (and later to melatonin). Hence, less carbs in the diet leads to less insulin which leads to less serotonin. This could cause vasocongestive type headaches.