The screw is for holding the tuner to the guitar? I envisioned the screw that holds the gear in place. A metal screw, holding metal to metal. Or am I wrong?

If it's a wood screw, go to a decent hardware store and match one of the others (yes, screw up your courage [pun noted] and take out one of the others for comparison). A small brass screw should not be hard to find.

And 50 years is surely vintage. I think eBay says "pre-1980" or some such year. I think antique dealers use 25 years as the cut-off, or used to, anyway. What model is it, and what kind of tuner? I'll look in my junk box.

Bob