Please do, and please let me know what you find, and if you don't mind, please measure the part of the clamp that would go inside the grooves on either side of the V block.
The reason I am asking is because I noticed that your clamp is taller and not exactly the same shape as mine. My clamp has no markings. Curious, I just did a little mini research deep dive on V blocks in vintage catalogs (1938 Starrett, 1948 Starrett, 1946 Lufkin, and 1938 Brown & Sharpe) and made an interesting discovery.
The V blocks with a 1" capacity (distance between the set-screw and V, or maximum diameter of rod that will fit in the V) that Starrett, Lufkin and B&S made in this era are virtually identical in design, shape, and dimensions (1-5/8" long by 1-1/4" high by 1-1/4" wide), with the same or at least very similar groove for the clamp. And believe it or not, the clamps in the catalogs look identical in style, shape, and dimensions as well. (Two of them either copied off the originator, or they all used the same fab shop.) Anyway, my point is I think the clamps may be interchangeable, which is a long way of saying my clamp may actually have originally belonged to a Lufkin or B&S pair of V blocks.
EDIT: I am not going to turn this into a machinists' accessories thread, but for a visual reference for my findings above, here are some vintage catalog scans...
Again, your clamp looks a little different (again, taller and no thickening where it clamps on to the V block), and may be newer, or possibly the same vintage but a different mfgr, so I am genuinely curious.
Thanks.
Thanks, Drives. As I alluded to in my comments above to Lefty, I'm actually not sure they go together by brand, but they are certainly a functional fit. I need the second V-block and clamp for a set!