If I recall correctly, in-text citations using the MLA style uses just the author and cited pages. Year is not included – which explains why Endnote’s MLA output style omits the Year field for the Author (Year) Citation template and why you are unable to display just the year.
As a workaround you could “hide” the author then manually type in the year. If working with the temporary citation doesn’t work you might try switching to the menu-driven commands. Information on editing temporary citations is available in the Help menu within the Endnote toolbar.