Interesting for certain.
What is the overall diameter as well as the diameter of the "cork" portion that fits inside the bottle mouth? I am thinking this would be for a medicine bottle..my hunch.
I am thinking this could be made of gutta-percha. Likely later 19th century or early 20th c.
Identifying the product or brand is a matter of finding a labeled bottle that happens to have a similar likeness of the man, or if you are lucky finding an actual bottle with this same cap in place.