I know that the correct phrasing for this sentence is, but I don't know why.
Many of the volunteers had already shown some early signs of mental illness.
Since the illness is unspecified, shouldn't it be illnesses? Mental illnesses can be counted:
This person suffers from two diagnosed mental illnesses.
So why is it we say "early signs of mental illness" as opposed to "illnesses"? We're talking about an unspecified group of people which may or may not have a certain condition or several conditions.
Policy limitations for mental illnesses typically limit benefits to 24 months if the disability is "caused or contributed to" by a "mental illness.