An excellent question, Russ. "Bull Hill" is normally used for Mount Taurus, the ridge just to the south of Breakneck, but that's in completely the wrong place to be the one referred to. Since Turners is the old name for Harriman Station, the site presumably lies somewhere in Harriman State Park. Looking at the maps, one assumes the proposed railroad would have more or less followed the route now occupied by Route 6. Given the textual clues (about 8 mi. east of the junction with the Erie, about halfway from Harriman to Fort Clinton) and looking at the topography, the tunnel would probably be at the crossing of the Long Mountain ridge-between "Long Mountain" and "Cranberry Hill" as shown on the NYNJTC trail maps. It looks like the Long Mountain Parkway (Route 6) has undergone at least one bout of realignment to reduce curvature, so the tunnel remains might well have been wiped out in the process. Unfortunately, most of my resources on the area, including Otto's book, are stored elsewhere at the moment.
There's a lot of stuff out there that isn't shown on any map. Hikers find undescribed mines and prospects in the park now and then, and I spent some time tramping around to the east of the tunnel location, looking unsuccessfully for the old Queensboro Mine, which presented fairly extensive workings to hikers in the 1910s.