Purely by accident, today I noticed that my wife has an artsy-fartsy shaped pump-spray transparent bottle of perfume on the bathroom sink counter, whose transparent top is almost identical to the Original Poster's mystery object, except its color and "outer" shape are a bit different. The only marking on the perfume bottle is "Dali" -- as in Salvadore Dali. The larger end of the "double tapered" hole in the top's underside fits over the neck of the bottle, and the smaller hole above it fits over the push-down pump knob. There's no need for the "double tapered" hole to be in an inkwell top.