Currently Salesforce does not have search layouts enabled for Email Message Object.
Which brings in lot of restrictions , such as if a field is not to be shown in global search is still being seen.
This is very critical when the data is very sensitive to the End Client .
Data can be email address which is not to be shown .. but currently that is not possible.
Also we cannot give permissions using profiles for the Email Message.
So please add search layouts for Email Mesage Standard object.