Concept: a version of Havelock Vetinari with some kind of lifelong chronic pain condition. Hear me out.
A lot of elements of Vetinari's character could be explained and actually made more interesting by chronic illness. At least in my experience, living with chronic pain forces you to develop a degree of control over your body (e.g. not freaking people out around you by visibly being in pain all the time through facial expressions / voice tone), it can give you a ridiculous pain tolerance, and for some people puts you in a position where you end up with a strong internal fortress which is relatively unshakeable by inconveniences of the physical world, similar to Stoicism in its original ancient philosophical sense -- even when your body is completely going to shit with a million symptoms, you are still Yourself, and you remain rational.
Basically, in short, some people react to chronic pain by becoming a rock in almost all situations.
Now, Vetinari is a man who can be calm when being imprisoned and theoretically having his life in danger; he is able to remain rational and make reasonable decisions when having literally just been shot; and he is able to tolerate the discomfort of being poisoned whilst not allowing the inability to care for himself to affect his internal sense of self. His reactions could for sure be the result of years of training and immense self-discipline (which is the textual implication), but I think it adds a layer of something interesting if he has built up a tolerance to physical and situational discomfort through being in agony for the majority of his life. If this is the case, then I think it's really cool that his disability would actually make him a better Patrician.
As an added bonus, I think this interpretation gets extra fun when you bring in the fact that he's very pale and skinny (pain and other chronic symptoms can affect appetite, and the paleness is kind of self-explanatory), and the fact that he doesn't sleep much (pain-somnia).
Idk. I find it fun to imagine that not only is he resilient and level-headed in the face of crisis because that's the kind of person he is and has trained himself to be, but that he has been forced to become that way by a body which doesn't give him any other choice, other than to simply give up.