Hi,
Thanks so much for your report!
The separator dropdown is not a CSS property, but adds an html element and therefore cannot be stored within a class or an ID. The styles, however, can, as you can see from your screenshot:
The width and height are entered for the selected class. Enclosed is my example, in which I have styled on .myHeadingSep. As you can see, the styles are attached to my class.

Long story short: you can save the styles of the separator in a class, but you have to add the separator itself (its HTML element) manually using the separator dropdown.
Best regards,
timmse