I found this very valuable article in "The Lady" magazine:

Chewing gum has a useful therapeutic value for those troubled by the discomfort of a dry mouth in stimulating the salivary glands to flow. Recently, in an ingenious piece of lateral thinking, Canadian Neurologist Dr Mandar Jog, has shown that it also has the reverse effect in reducing the excess saliva (which often results in drooling) that is a common feature of Parkinson’s disease.
The rationale is as follows: the many disturbances of function associated with this (and similar) neurological disorders include reduced frequency and poor coordination of the swallowing reflex, with the result that saliva “overflows”.
Dr Jog speculated that chewing gum might mitigate this by stimulating the reflex to work more effectively – so though it would generate more saliva, this would be more readily cleared. And so it turned out as he recently reports in the journal, Neurology, concluding that chewing gum “is a cost-effective, self-managed approach” to reduce excess saliva.