I think the fact that this is a problem that comes only when you are under pressure means that it is most likely just to be a nervous tic. In other words, if your eyes do not do this when you are not under pressure, then it is not likely to be a major medical problem.
However, nervous tics can be serious social problems, as they can be embarrassing to you and can also have a bad effect on the impression you give while performing under pressure. Many times, nervous tics can be controlled if you learn how.
You may want to talk to a psychologist
or a therapist
about these tics. Learning to control the tics involves learning to control the anxiety
and other stress emotions that bring them on. A psychologist or therapist can teach you relaxation techniques as well as cognitive techniques to control anxiety and reduce the chance that the tics will emerge.
Furthermore, general relaxation and stress reduction techniques may be helpful to you. These can include regular exercise, a regular sleep routine, and healthy eating. Taking control in these areas of your life often will have a major effect on the anxiety that you feel while on the job.