I have a plastic spacer between the head and motor that pumps out the head. There is a slot on the bottom side of the plastic piece that is leaking when any liquid is put into the bowl of the head. Motor seems fine and is working.
It sounds like you're describing the bowl gasket. It's rubber and rubber does eventually dry out. So I think a new one should solve your problem. If you can give me the make/model/age of the toilet, I can give you a link to the owners manual that includes an exploded drawing and parts list so you'll know what to order.I have a plastic spacer between the head and motor that pumps out the head.