If you had posted both pictures and said they were used by ladies, I might have thought it was for catching the skirt train when dancing... However! I will go real wild and suggest it is a hat hanging device, to be slipped over the brim to allow it to hang on a hook. Makes more sense than men needing to catch up their train hems in the 1880's.
Yes, you've nailed it. It's a Ball Programme Holder and Marker, patented by Frederick William Powell of 23, Great Sutton Street, Clerkenwell, London in 1886.
When first looking at this, wondered for a moment if it was small press-style check-protector...and from the description, sounds like the marker does stamp or press the name or initials into a dance card rather than holding an "old-fashioned pencil" (or am I not understanding correctly?).
Hunh, would love to see one and try it out; wondering how personalization was offered with a 24 hour turn-around - tiny type that set in? I have little luck searching British patents, but perhaps someone has one and can show it...