Wow! My favorite bottlenecker (whatta vibrato!!) and second favorite singer (Elmore holds the #1 spot) in blues music!
Not to further beat to death the tired "the tone in the hands, dude" mantra, I imagine if Robert walked into your gig today, and sat in on your reissue whatever plugged into your boutique whatever, it would still sound pretty much like Nighthawk.
Robert Nighthawk was from my home town. I grew up listening to this kind of stuff -- Sonny Boy Williamson was still playing around town when I was a kid -- and, fifty-plus years later, have never gotten away from it. I play a lot of different music now, and a lot of different instruments, but I always go home to blues.
Heavy strings, high action, and single-coil pickups would be a good place to start...and a small tube combo amp, cranked up.
But, yeah, it's mostly Mr. Nighthawk...I've owned a couple of Gretsch Corvettes, and I play passable slide, but I've never been able to make a noise quite like that...