I also discovered a parallel effect that at least in my case is a bigger issue: if you strain while thinking, you can end up engaging head muscles which can fatigue quickly and become painful. For me, thinking hard hurts and I thought it was a brain thing, but now I think it's primarily strain-related tension headaches, which oddly can feel like a brain thing.

So from my experience there seems to be a possibility that when you think you are having brain tiredness you're actually having a physical headache.