Does anyone have any idea what this might be? It is at least insulator related, in the sense that it was made by an insulator manufacturing company.
It is about 3 1/4" wide across the umbrella, 2 1/4" wide across the cylinder, and about 3" tall.
The cylinder portion is very regular -- obviously machine formed, as is the hole through the piece. The umbrella is very irregular and looks hand made. In fact, you can see a number of finger prints around the umbrella, including a couple where you can see the whorls and ridges well enough that the FBI should be able to ID the person who made it!
The cylinder and underside of the umbrella is unglazed. The top of the umbrella is a speckled brown color, but it's not "smooth" like a glaze usually is and I'm not 100% sure what gave it the color it has.