Regarding the translation of béal as mouth, it is very possible that the béal referred to is the edge or mouth of the pot or cauldron, rather than the rooster's beak. Both interpretations make sense, since both referents, the rooster (an coileach) and the pot (an pota) are masculine nouns.
This has not prevented many Raidió na Gaeltachta announcers from feminizing the rooster (a sign or our times?) by leniting the noun after the article (an choileach)!