The Dowsing Rod is an item used to find missing or hidden items (such as buried water for a new well). They use the technique of divine effort (and hence the other name Diving Rod) to find the items or water locations, but its scientific logic is doubted.
In the Raven's Cove Story Quest, Dr. Bellrog orders the pirate to find the 3rd idol hidden in El Patron's Mine long ago by the dog of El Patron's Crew. The rod has to be constructed first, by gathering the teeth of 13 Fire Bats. Clicking the Dowsing Rod button tells the location of the item from the character's position. The location it guides you to are dig spots. The Dig Spot however may not be the first place to find the idol, and so the rod takes the player to other locations if not found in one place.
The dig spots of the mine are marked in the following map: