OK OK I spotted the Bullet Hole you are asking about. It is a 2920' false summit (or the 2860' notch between this summit and the rest of the Beaver Kill Range). It is just north of the Dog Hollow and south of the Beaver Kill. The Bullet Hole is not labeled on the NY/NJ trail conference maps, but is on the USGS quad and on map in the AMC Catskill Mountain Guide, by Peter Kick. The AMC guide book mentions that the private land enclave to the southeast is leased to a hunting club. Maybe that has a connection to the name Bullet Hole. Or perhaps from some nearby mountain the notch resembles a bullet hole in the ridge.
The AMC guide book mentions that the Neversink Hardenburgh (NH) trail crosses a road just east of the Gulf of Mexico brook and west of the Vly Pond outlet. Michael Kudish's book mentions that the recent logging road (circa 1995) follows the Gulf of Mexico brook through a narrow strip of private land (probably the eastern of the two strips shown on the trail maps). It sounds like these two roads are the same, and you should be able to follow it all the way up to the old ridge road that goes to Graham. You might have an entirely trail route - if that is what you want. It also brings up the subject of permission to hike Graham which is still owned by the descendents of Jay Gould, the famous railroad baron. Permission to hike Graham may be obtained from the caretaker, William J Scholl, Dry Brk Rd, Arkville, NY 12406, 845-586-4056. He would also be able to advise you whether the Gould family owns that strip of land containing the logging road.
