There are no separate drop shadow options for text and text outline, only for objects and objects outline.
But there are workarounds.
Potential workaround: once you're absolutely sure the text is correct (size, tracking / kerning, spelling, grammar, etc.), select the text container, copy, paste in place, move to back. In the Swatches panel, click the "Formatting affects type (T)" icon to change the color of the type. For fill, select None. For stroke, select Paper. In the Effects panel, select Text and apply your drop shadow, adjusting the color, blending mode, opacity, offset, and size. It would be a good idea to "Allow object-level display settings" under Display Performance, and make sure you're looking at the object in High-quality display (if you don't do that already).