What you're seeing as a tripod socket is half of the "pin and screw" flash mount. The Hawkeye has no tripod socket, though it's easy to add one. Get a piece of 1/4" poplar, one inch wide, at the nearest Home Depot. While you're there, get a "blind nut" in 1/4-20 size and a cheap hot glue gun and some glue sticks for it.
When you get home, cut two pieces of the poplar to size to form a "T" shape on the bottom of the removable back part of the camera body. In the one that will be crosswise, drill a centered 5/16" hole to accept the center shank of the blind nut, and insert the nut into the hole -- if it's the "drive in" type with sharp spurs, put the wood on a flat board or similar and drive the nut home with a hammer; otherwise, leave it loose; we'll lock it in place on the next step.
Now, heat up the hot glue gun and use it to attach the two sticks to the bottom of the camera -- there'll be a little clearance under the front one where the plate of the blind nut contacts, so install that one first; hold it in place and squeeze hot glue under the edge. Once it's in place and the glue is set up, do the same with the lengthwise stick, leaving the same spacing under the stick when you glue it in place. Last thing before putting the glue gun away, put a small dollop of hot glue on the bottom of each stick at the ends of the "T"; these will act as feet and let you steady the camera without a tripod (for a low point of view, etc.). Let these partially harden, then press them against a flat, smooth surface to give them even, flat bottoms (but don't leave them in contact for long until completely hard).
Ready to go! Oh, BTW -- after using it a bit, you'll probably wish for a cable release socket -- good luck! One potential trick; use a small block of wood and very strong rubber band to hold the shutter release down, so you can take your hands off the camera for long exposures. A small plastic clamp might also work.
