This term bothers me. Such a creature as I described above is not, technically, mindless. It's clearly capable of thinking - just in a very simple and inflexible way. A typical horror movie zombie can do things like processing sounds and orienting towards them, (clumsily) coordinating their body to move towards the sound, feel hunger and know that biting something is what they should do about it, etc. All of those, though they seem very simple to the average person, become very complex if you look closely at what is needed to do it. For example, do you know how many muscles have to move in perfect timing for you to take a step? A lot. (Incidentally, the only way a walking, attacking zombie could be mindless is if it's controlled by a necromancer or something.)
I see this in real life, too. I can't count how many times I saw someone refer to Terri Schiavo or other people in vegetative states as 'brain dead' - even though, by breathing, having reflexes, etc, the person is proving that some parts of the brain are working just fine. And recent research is suggesting just how hard it can be to rule out complex cognition in a severely brain-injured patient.
There seems to be this idea in people's heads of an 'empty shell' - an animate body without a person inside. We seem determined that there must be someone who is like this, whether in fiction or in real life. And we keep applying this idea to all sorts of people who can't communicate and lack various other skills.
It's theoretically possible that there is someone out there who has a functioning autonomic system but no cognitive skills whatsoever. But we have no proof of their existance. And meanwhile, we keep projecting this image onto people who are aware and reacting to their environment, but processing in very atypical and/or extremely simple ways.