I think that mild dehydration is a major reason for the headache. If that is the case you will be the most dehydrated at the end of the fast having gone the most time without liquids. I don’t think that hydration instantly kicks in the second you break your fast so your body will be the most dehydrated as you are breaking it.
Other reason could be a sugar levels spiking. If you are eating lots of carbs after not eating anything you blood sugar (even for non-diabetics) could spike and maybe cause a headache.
Disclaimer: I am not a Medical Doctor and this could all be totally wrong. Just a guess.