The "PEM" post mental exertion is very different from the "PEM" post physical exertion and I wish more people would acknowledge this.
I personally do not experience any excess physical fatiguability after mental exertion (say, a Uni exam) over the next few days, provided I had sufficient sleep and so on. The only physical issues relate to the muscles that were used, eg eyes, hand/arm.
But if I was to physically exert myself, then this leads not only to physical fatigability, but also extra mental fatigue and brainfog over the next few days.
But I agree, it is not about reaching some sort of magic "anerobic threshold" heartrate. PEM can be induced without reaching this threshold heartrate. The tight coupling of heart rate and anerobic threshold only occurs during a ramped increase in exercise output (like on a CPET test).
The brain uses a lot of energy, and the two main hypotheses that explain the 2 Day CPET findings - endothelial dysfunction and afferent nerve peripheral sensitisation (potentially type II, III and IV fibres - Alan Light and others have investigated this sensitisation) and their spinal feedback loops do have analogues in the brain. The purpose of these afferents is inhibitory feedback, to increase predictability of output, when there is something unusual going on peripherally that leads to inconsistent performance, such as fatigue. The headaches also strongly suggest vascular involvement.