I don’t understand this connection between the words nose and narc. Surely the former derives from a Latin word (nasus) and the latter as an abbreviation of narcotics?

We should also be aware of the positive connotations of nose, as for example suggested in def 6 in MW10:

b : a knack for discovery or understanding <a keen nose for absurdity>
- on the nose 1 a : at or to a target point <the bombs landed right on the nose> b (1) : on target : ACCURATE (2) : ACCURATELY 2 : to win -- used of horse or dog racing bets