@Snow Leopard brains operate in these regards .
I believe I have much greater mental endurance than most people (it might be genetic, my father is an ultramarathon runner). I had a very long attention span before I first became ill. I can push quite hard mentally (learning how to concentrate with ME is very difficult...) or physically. Naturally there are consequences. I can push up to a point, dealing with the extra pain, but pushing too hard and my ability drops off a cliff walking becomes difficult, or I literally cannot solve anything requiring intelligence (is a real problem after two hours of a science exam), or I feel dizzy, about to pass out and.
But while mental expenditure sets me back days in terms of mental fatigue, it does not seem to increase the fatiguability of the rest of my body (example: after a uni exam). On the other hand, exercise does increase my mental fatigue. Since I experience a headache 24/7, for over a decade, I kind of use the severity of my headache and (in)ability to concentrate as a gauge for my level of mental fatigue.
Other experiences, like trying to read a book in 4 days (Pratchett's "long war") has led to more than 4 days of extremely sore eyes and increased mental fatigue.
As far as effects of emotional exertion, anxiety, go, the experience may to some feel like fatigue, for there is a sort of 'dull' or 'numb' feeling, reduced concentration and increased drowsiness. Maybe this is a dysthymic feeling, I don't know, but it feels quite different to the day to day fatigue.