Typically this medicine is a little too thick to go down their nostrils, or they would just force it out.

If you mean offering them a drink to get them to smack and open the mouth...you could try. But in my experience when you approach them with something they're going to clam up. It's worth a try to see if you can get a credit card or something in there, but the timing would have to be right on...or your back to my idea, cause they probably ain't gonna open their mouth again for a while if you miss.
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"A man that should call everything by it's right name, would hardly pass the streets without being knocked down as a common enemy." The Complete Works of George Savile, First Marquess of Halifax 1912,246