I managed to stumble upon both pieces of the blade, but never actually got the quest to go look for them. Tarquin never showed up at Stonegarden; he's back at the Lady Vengeance, giving me some generic dialogue.
Am I out of luck? I tried putting the artifact together myself, but alas, the only thing I managed to accomplish is confirm my suspicion that potatoes aren't the appropriate material to reforge an ancient artifact.