I watched that for ages
it's a beautiful piece of glass.
I did wonder if it might be Bohemian sort of turn of the century. It reminds me of a perfume bottle I have that is still as yet unidentified, but there were a number of makers who produced this deep amethyst glass at that time including a German maker I think. Sorry memory fails me on giving names at the mo and I've not time to look them up.
So that could fit in with Christine's suggestion of comb tray or it being part of a dressing table set.
You could try searching for amethyst facet cut vase and it might throw up some makers for you to investigate a bit more (including searching on here for Bohemian facet cut vase as that might also throw up something).