Tiny glands in the ear canal produce cerumen cerumen /ce·ru·men/ (se-roo´men) earwax; the waxlike substance found within the external meatus of the ear.ceru´minalceru´minous
ce·ru·men
n.
I am pretty sure that there is no mucus membrane tissue in the ear.
The mucous membranes (or mucosae; singular mucosa) are linings of mostly endodermal origin, covered in epithelium, which are involved in absorption and secretion. They line various body cavities that are exposed to the external environment and internal organs. It is at several places continuous with skin: at the nostrils, the lips, the ears, the genital area, and the anus. The sticky, thick fluid secreted by the mucous membranes and gland is termed mucus. The term mucous membrane refers to where they are found in the body and not every mucous membrane secretes mucus.
Note the last part. You can have a mucous membrane that doesn't secrete mucous.