Has it occurred to you that Listerine is named after Joseph Lister, who we learned (when? junior-high biology?) was the inventor of antisepsis. Listerine was named in 1879, when Lister was still alive and working, so the association was presumably livelier than it is today.
The -ine in Listerine has the sense, from chemistry, of “forming names of alkaloids, halogens, amines, amino acids, and other substances” (Oxford American), and we see it around quite a lot—chlorine, for example, from khlōros, green, and -ine (likewise iodine is ‘violet-colored’).
Cocaine, then, is coca-ine, relating to the alkaloid from the coca leaf. It looks like it should be (and is) pronounced co-caine, though. And co-caine in turn influenced the likes of procaine and novocaine, synthetic anesthetics that replaced the earlier use of cocaine for the purpose.
And let’s not forget caffeine, from the French, café-ine.