The trailhead for this can be reached by car by turning off the Whipple Observatory Road onto the Agua Caliente Road. There is a car park area at the trailhead. After parking, look for the trail about a hundred feet back down the road on the right.
The trail is singletrack for about one mile where there is an intersection with a 4x4 track which heads off to the west; turn right to stay on the trail. Follow this for 0.8 miles where you'll see a mine vent on the right at trail level. The mine (unknown name) is over the cliff in the same area.
At approximately two miles, there is a small trail off to the left. This trail leads up the back of Elephant Head. Continuing on, you'll be able to see the mine tailings from quite a distance. A use trail circles the mine opening which has been buried and the vent, which is open (be careful) and comes back to the same point. Follow the same track back to the parking area.