I've taken a pause before looking properly at the last two papers. But, as you've mentioned it, one is on headache and the other migraine (
Migraine associated with conversion disorder (Babinski's migraine). Analysis of a series of 43 cases - ScienceDirect )
The headache one:
Functional/Psychogenic Neurological Symptoms and Headache (rwevansmd.com)
has a big old spiel bit about whether it is functional and the reasons why physicians mightn't be keen on seeing their headache patients that way
"What If Functional Neurological Symptoms Were Considered As Legitimate As Migraine?—For both these cases, the problem may lie in the fact that many neurologists have difficulty taking seriously or believing patients with functional weakness and dissociative attacks. There is still widespread support among neurologists for the idea that deception is playing a part in these symptoms even if they do not think it is the whole story.10 Certainly, 64% of the respondents of our survey agreed that these patients often deliberately exaggerate their symptoms (see Appendix I). This may be in large part because of the way that functional motor symptoms in particular can be shown at the bedside to be inconsistent (whereas there is no similar test for headache). No wonder, then, that headache specialists do not want “honest” headache patients to be associated with “dishonest” functional/psychogenic patients. Only 9% of headache specialists thought that patients with headaches exaggerate. But imagine how much more interesting the debate would be, if both types of symptoms could be taken equally seriously. In that scenario we could ask much more interesting questions not only about the biology of functional neurological symptoms but about the psychology of headache."
