Chambers Dictionary suggests the name of the �mullet' hairstyle may be from the dialect word 'mullethead' meaning 'fool'. (Incidentally, it says it is ... "a hairstyle that is short at the front, long at the back, and ridiculous all round".) So, the editors clearly considered the style somewhat foolish!
In American English, a mullethead is a flat-headed fish and here's a quote from there in an edition of Harper's Magazine published as long ago as the 1860s about it, "Dat fish is a mullet-head; it hain't got any brains."
It seems, therefore, that the fish's cranial flatness matches the shortness of the hair at the front of the mullet-wearer's head.
It would certainly appear that the idea of daftness regarding the mullet - whether fish or mammal - exists on either side of the Atlantic!