OK, I've been working this out myself with the aid of the NYS 1-m DEM, and I think I have things sorted out at last. (Looking at the current OSM relations, I think I did this before, and forgot...)
The original Sunk Mine Railroad, or West Point Railroad as it's called in the 1868 Beers Atlas, began on the northwest side of 301 at "Dump Hill", and ran obliquely across the front of what's now the Cold Spring Institute to the junction with what's now the yellow-blazed Old Mine Railroad trail (east end of OSM segment 187355071). It then proceeded south along that segment. Somewhere around the stream crossing, the current trail bears right and climbs the shoulder of the hill; the railroad went straight across and is now submerged under John Allen Pond. The blue-blazed Three Lakes Trail briefly picks it up on the other side of the pond as it runs northeast, but then continues northeast towards the junction with the Charcoal Burners trail and Hidden Lake, while the roadbed curves to the right to make a horseshoe upslope of the stream draining the pond. As the roadbed turns southwest along the side of the mountain, it passes the mouth of the Hamilton Mine, crosses Sunk Mine Road just east of the stream, and swings into another horseshoe around the point of the mountain, recrossing Sunk Mine Road and heading northeast along the base of the mountain to terminate at the Sunk Mine. (This would be that area of parallel road/railroad grade.)
The other segment of the Old Mine Railroad trail (OSM segment 181686470) is apparently part of the uncompleted Canada Mine extension. It looks like this was used as an access road from 301 to Hidden Lake, which might explain the wider right-of-way; there's something that (from the armchair) might have been a borrow pit for doing so about halfway between the red trail and Hidden Lake. The grade then skirts the northwest side of Hidden Lake, with the remains of what must have been a fill-and-trestle system crossing the inlet, and heads northeast until it runs into the AT, which follows the grade to 301. While there are mine openings just above there, across Canopus Creek (the Phillips Mine), I presume it extended somewhat further north but the grading is flooded.
I hope this is useful in placing a written description of the route on record. There's some assertion in old message board forums that the West Point Railroad was standard gauge, but I don't see why it would be; I presume the whole operation was narrow gauge and compatible with the mine cars in the connecting mines.
This article of 1892 may be of some interest: https://newspaperarchive.com/brewster-s ... -1891-p-1/
It covers Thomas Edison's charter of the Westchester and Putnam Railroad to haul iron from this chain of mines to Peekskill. The Peekskill Iron Company's railroad already extended from Peekskill up to the Todd and Croft Mines. According to the article, grading from the Croft to the Sunk Mine would have been to standard gauge width, but it would have been laid initially as 3' gauge, the existing Peekskill Iron Co. line being 2' gauge.