I am creating a new role. How can I add permission for users to be able to search a customer's name and email address in the global search?

not a permission - you'll need to add a custom field with the global search button checked for them to record the email into

In order for a user to see the Global Search field, the administrator needs to add the Perform Search permission to the user's role and set Level to View (at least). Some standard NetSuite roles like System Administrator do not have this permission by default.