A fellow visitor asks our guide, Liam, where the widest road on 14-km-long Inishmore might be. "You're on it," he says cheerfully as we resume our day trip, one of many that RailTours Ireland runs ...

INISHMORE ISLAND, IRELAND—On a small Irish island, a world-renowned fashion accessory is produced, not by mechanized factories, but by knitting artists in an age-old, local tradition.