I'm starting to call it "cognitive empathy". Rather than having emotions and theory of mind operate in the limbic system where they belong, and not having the option of not having an empathic center, the mind starts to build its own version of the limbic system in the forebrain. This brings the functioning of that system into the cognitive purview.

It's definitely in the Cluster B 'spectrum' but in order to make sense of it I think the best approach is to understand where in early development mind started to get disordered, and just how 'off' you really are.

Autism Spectrum Disorder happens extremely early, while the mind is developing. Only the precisely correct form of early intervention will restore some degree of normalcy to the person.

Personality disorders are not quite as dramatic, and start to develop in childhood. Traumatic things happen to you that affect the way your brain develops and it deeply affects you all the way down to your basal ganglia. The amygdala has the ability to completely override the forebrain and cognitive processing, so when it malfunctions, or is disordered, it seriously affects your ability to function in society.

What I'm calling here 'cognitive empathy' is when the trauma doesn't really reach the point where it affects functioning. The person knows something is wrong but can't put a finger on it. What's happened is rather than trauma pushing all the way down into the reptile brain / basal ganglia, or so deep into the limbic system that it rewires or completely turning emotional processing off, (psychopathy) the person gets 'shadows' of emotional processing that they then need to 'shore up' with cognitive processing.

Those with personality disorders don't really have a choice other than to develop a 'mask'. Their emotional centers just don't function well enough, no amount of watching sad anime will cause any form of feeling to arise. Normal people are really sensitive to the subtleties of emotional response hitting your face, and so psychopaths simply can't have a 'normal' conversation with people unless they 'put on their masks'. The mask is a wholesale cognitive recreation of the limbic system, crafted over years of getting it wrong until they finally figure it out.

I think most people that describe having cognitive empathy aren't this badly damaged. Their limbic systems function, just not well. They can improve, often just by seeking out feeling wherever they can find it. So many people describe operating cognitively until one day in adulthood they managed to start processing, then all of a sudden it's like a new world opened up for them. It's their limbic system finally making connections with the forebrain. They have to keep working on it throughout their lives to increase the trickle into a working and healthy interconnection.

Really good empathy involves lots of back and forth communication between the forebrain and the limbic system. Empathy that's only cognitive needs to be controlled and extreme anxiety results when the control isn't maintained. Anxiety results when you get amygdala activation as a result of a feeling of lack of control. It overrides your forebrain and places in the forefront of the mind, "get back to safety." With good limbic system function then the person can better orient themselves in uncertain situations. A lot of this is due to empathy, the 'mirror neuron' system. You can look around, sense that no one is trying to judge you or anything, and start to relax. But if all that is happening cognitively, it won't happen fast enough to keep up with the amygdala's defense mechanisms.