A conductor is a quest item used only in the Creature of Fenkenstrain quest. It is obtained by melting a silver bar in a furnace with a conductor mould in the player's inventory. This requires level 20 Crafting. It is used to repair the conductor upstairs in Dr Fenkenstrain's castle. Players can make these after the quest; however, they are useless once the quest is complete.
Considering that the Creature of Fenkenstrain is a parallel of Mary Shelley's Frankenstein, it is highly likely that the conductor is meant to animate Fenkenstrain through the use of electricity.