But Dr. Geschwind is quick to note that his finding was not merely serendipitous. Quoting the 19th-century scientist Louis Pasteur, he says: ''In the fields of observation, chance favors the prepared mind.'' Dr. Geschwind's mind was prepared to look at the full spectrum of autoimmune disorders among left-handed people and among dyslexics on the theory that a genetic predisposition to a condition may be expressed differently in different people. Studied Left-Handers' Problems

Instead of studying the incidence of left-handedness among dyslexics, as most previous researchers had done, Dr. Geschwind decided to study left-handed people to determine what problems existed among them and their families. With the help of Peter Behan, a neurologist at the University of Glasgow, he devised a questionnaire that would select those people who were most strongly left-handed and compared them with strongly right-handed people.

On average, Dr. Geschwind believes that about 70 percent of the population has standard brain dominance, with the left side of the brain controlling language and handedness, making most of those individuals right-handed. The remaining 30 percent of people have more symmetrical brain dominance, and of these about a third are strongly left-handed.

In the first study, involving 253 left-handers (gleaned from patrons of a shop for left-handers in London) and an equal number of right-handers, the left-handed group was found to have 12 times more learning disabilities and nearly three times more autoimmune diseases. Their relatives also had higher rates of these problems.

In the second study, the subjects were gathered from among the general population of Glasgow. Here too, the incidence of autoimmune disease was two and a half times higher among the left-handers. A third study compared the frequency of left-handedness among patients with migraine headaches or immune disorders with the handedness of normal people in Glasgow. A higher percentage of left-handers was found among the headache patients and those with myasthenia gravis, an autoimmune disease. Dr. Geschwind believes that some cases of migraine may result from an immunological disorder. Allergies More Common

In new studies not yet published, the researchers found ''a distinct increase in childhood allergies among strongly left-handed people.'' Other researchers have reported a high rate of allergies among stutterers, an increased frequency of food allergy among hyperactive children, and a high rate of immune disorders among children with autism.

''In all these conditions there is an elevated rate of lefthandedness,'' Dr. Geschwind reported to a conference this month, and that suggests the possibility of a common origin.