What exactly is "composition"? Is it some kind of hard rubber or....?
Excellent question!
"Composition", in the days before modern plastics, was any amalgam of various insulating materials, usually rubber, plant fibers such as wheat straw or cork, minerals such as mica or asbestos, all ground up and mixed together. There were undoubtedly hundreds of varieties of substances all going under this name, and they were not used solely for electrical materials. Dice, chess pieces, inexpensive tableware, toys, tourist souvenirs, you name it.
If it looks and feels sort of like hard rubber, but you can see fibers, it's probably "composition".