By what mechanism do cough drops work...or don't they?   Sucking on a cough drop and swallowing the product, it goes down the esophagus which leads to the stomach, but it seems to me the cough is located in the the trachea which leads to the lungs and no liquid normally goes down there.  Therefore, how can sucking on a cough drop have any effect on the irradiation in the trachea where the irritation that causes coughs originate.  Are the fumes from the medicated (or unmedicated) cough drops inhaled and as such deliver some soothing vapor, or are cough drops a placebo plain and simple?

Menthol can act as a numbing agent for general throat irritations.

If I had a cough associated with other cold or flu symptoms, I'd take a better all around medication. For a cough by itself (from a tickle in your throat), I think anything that keeps your mouth and throat moist will work. 

I don't really think cough drops are very effective, but the mechanism is probably to relieve as much irritation as possible before the trickle of saliva & medications gets to your esophagus. You're right, once it gets there, the mechanisms for removing unwanted irritations involve less coughing and more vomiting.

It could be part placebo too. I know when I go to weddings, plays, and funerals, I take some mints to suck on to keep my throat moist. It seems like the tickle always happens when you're supposed to be quiet, so there may be something psychosomatic going on there.

2 hours ago, Bushranger said:

effect on the irradiation in the trachea

I hope this was a spellcheck mistake.