What do I think a headache is? Well it isn’t evidence of blood clots if that’s what you’re getting at.
Headaches can be caused by dehydration, fatigue, sleep deprivation, stress, and any number of other factors. Infection, medications, all sorts of things. There’s not necessarily any physical cause at the site of pain. Nerve cells misfiring (due to any of the above reasons) or irritation or inflammation in or around the blood vessels anywhere in the neck or head area can all contribute. It’s an extremely non-specific symptom.
But no, a headache is not evidence that blood clots are sitting there.
You meant to say "not pathognomonic" didn't you?