It`s difficult to assign the item to a particular member of Habsburg family. There were many Archdukes born mid 19th century when JC Klinkosch worked. They had wives, daughters etc. And not only in Austria. Compare with Duchy of Modena (Ducato di Modena e Reggio) House of Habsburg-Este
http://www.almanachdegotha.org/id128.html
I have cut glass set with Habsburg coat of arms engraved;
not very likely it comes from Schönbrunn Palace.
The coat of arms shown here is stamped. One does not make dies for a couple of items.JC Klinkosch must have had a considerable order from Habsburgs, whatever family it was.
Regards