The Option Values for the hidden Configuration Characteristic can be added the same way you would for a Standard (not hidden) display.
The Configuration ID will consider the hidden Characteristic. Hidden Characteristics are still part of the Configuration Specification, they are just not displayed on the screen when editing or viewing the Configuration*.
*You’ll notice when you’re editing or viewing a Configuration that by doing a Right Mouse Button in the Header area of the screen will give you the option to “Show Hidden Rows”. By hiding Characteristics, you can have Characteristics being read against rules, but not be displayed for the user. This helps keep their interface clean, as you can choose to display only the Characteristics which require the user to make a selection, all while the background logic is being handled by hidden Characteristics which they don’t see unless choosing to.