Historically and in fiction the supposed signs of ‘psychosomatic illnesses’ overlap with the signs of ‘malingering‘ and potentially include:
- doesn’t make medical/scientific sense, eg paralysis when there is no evidence of nerve damage
- involves voluntary actions, but not reflexes, eg blinking when object approaches the eye in hysterical blindness
- inconsistent or variable presentation, eg a paralysis that disappears when no medical observer is present or disappears when needed to prevent a fall, or the presence of mutism when talking to some people but not to others
In the world of popular culture, if not psychiatry, these concepts grew out of Freudian Psychoanalysis and the First World War understanding of shell shock.
However, I don’t know if there are any clear cut demonstrable examples of illnesses involving the above, and in most real life situations things are much more complex.
For example to say something does not make scientific/medical sense depends entirely on our current state of medical knowledge and ignores conditions like MS that were previously understood to psychiatric but are now known to be neurological. Because a complex condition is currently poorly understood this is not of itself evidence that is psychosomatic. Also variability of does not necessarily mean a psychological basis, it may as likely mean we do not understand the triggers or causes of the symptoms. Because we currently fail to identify the patterns does not mean that patterns do not exist.