“Mucilage” is a word whose sound is wildly inappropriate to its meaning. In the world of adhesive nomenclature, “paste” is good and “glue” is even better. Polysyllabic mucilage ought to denote something far more serious -- perhaps an orthopedic procedure ("OK, let's mucilage that ankle").
In my life, mucilage made its mark long before glue arrived on the scene. Schoolchildren in the 1940s were issued small curvy bottles of the stuff, each fitted with a red-rubber tip which was slit so that a drop or two could be emitted when the bottle was pressed to the surface of your construction-paper or doily project. LePage’s Mucilage, I believe it was called. We said Page as "page" but surely LePage's Mucilage if pronounced Frenchly would be far more euphonious. Some claim that if you were building a model airplane, you would use mucilage on your fuselage, but I believe such an assertion to the kind of persiflage at which I take umbrage.
And yes, the word is a descendant and cousin of Latin mucus, meaning mucus.
Unbeknownst to 1940s me, mucilage has a life outside the bottle. It is a glycoprotein and exopolysaccharide found in most plants where it helps to store water and thicken membranes. I have now learned that the sticky stuff on the leaf tips of the insect-catching sundews that live at the edges of our pond is a form of mucilage.
I would be curious to know from what plants William Nelson LePage distilled the vast vats of mucilage that were diluted and parceled out to schoolchildren, who then spent the hour after "Arts and Crafts" removing yellow mucilage scale from their fingers. But I do now know why he got the contract -- because vegetable mucilage is, if not exactly edible, not poisonous either.