One last thing about the Nighthawks diner search, especially now that the Mulry Square triangle is covered in plywood, readied for its transformation into a subway ventilation plant for the MTA.
I followed up awhile back on a suggestion by author Jack Womack to take a look at the photo book New York Then & Now by Watson and Gillon. In it, they include the following photo looking south at Mulry Square, the triangle in question, in 1976.
The stone building in the left foreground is the old St. Vincent's Hospital. The blank wall is where the Barney's painted billboard was recently.
A close-up shows the White Tower (not White Castle) burger stand on the left side of the triangle, and the old Esso has become an Exxon. It further cements the evidence that the remaining structure in the empty lot today is a remnant of the gas station's garage and not of a diner.
The "mystery diner" is on the right with its extended, glassed-in dining room beneath an awning--before it gained a second story. While I can't read the sign, it doesn't look much like Nighthawks. It's another dead end, of sorts--but not for people interested in hunting down old White Tower burger joints.
Presumably, any remaining remnants of the White Tower and the gas station are being demolished by the MTA right now.