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Oh wow I get to be the one that answers for once!

You can trust your Google-fu, this is in fact a candle holder! The glass is for a tea light candle, and it sits on a base that's made of wire. The top of the wire is a U shape to hold on to the pointy end of the glass. I'll take a picture of mine and post in a reply to this comment.

My mom had an eyewash cup when I was a kid that looked kind of like this. Same color glass. It had a base like a wineglass tho.

My title describes the thing. As described: the object is a hollow "cup" in the shape of an elliptic paraboloid made of thick blue glass, roughly 3" tall and 2" wide at base. It has a shallow (~1/8" deep) indentation along exterior axis (longitudinal). The exterior indentation is too shallow to hold an index card or piece of paper.

I have already tried every combination of key word searches based on the description above. I also plugged the description into ChatGPT, and I did a Google reverse image search of the pictures.

I found two of these on eBay called "tealight holders". However, the object is not freestanding in a way that would hold a tealight on its own, and I cannot find any example of the "larger candle holder" one of the listings claims exists. The other listing descriptions is "?? not sure what this is. I thought it went to an old bird cage for the water."

I am skeptical to call this a tealight holder unless someone can provide evidence of it being used as such.

I thought it was some kind of eye-washing item. ^{..^}

I think it is the cover off a light. Like a boat light, or truck light … but the blue is throwing me off. That isn’t a color that is used for signaling. But it looks to me like it fits over a bulb, into a round base, and has a wire loop that flips over the top (into the slot) to hold it in place.

I wonder if it may be for an old electrical system? Like mounted on a transformer, or something? The blue could indicate that it is on, or operational. And if it was off that would signal a problem. The heavy glass makes me think of glass isolators on power lines that people collect…