Most gaskets, especially those that also served as valves, were made of leather more than a century ago. The old one may not look much like leather because it's been soaked with various kinds of oil for the past hundred years, but leather was used almost universally for this kind of application.
It should be possible to remove the old gasket (likely in tiny pieces), clean up the pocket, and cut a new gasket to fit from a suitable piece of soft leather (from an old shoe, purse, or baseball glove, football, basketball, or vollyball cover, if old enough, or what have you -- or from new leather, purchased from a leatherworking supplier). Select leather a little thicker than the depth of the pocket.
Glue it in place with rubber cement or contact cement, and once the glue is thoroughly dry, put some neat's foot oil or similar leather dressing on the sealing surface to keep it soft. Such a repair ought to work just like the original did when new, and with a little care, last another century.