Second pot of coffee hasn’t helped, and I’m flummoxed by these items.
Some observations (probably obvious to those who have looked at the pieces for 17 years...)
1. Location of holes. In the photo with the white background and the wood screw to the left of the two pieces (the ‘white photo’) the two holes in each piece appear to be parallel to the long axis of the piece, but slightly off centerline. I don’t believe this is significant - I’ve owned a few pieces of antique furniture that had hardware with similar characteristics (flaws?). I think it might suggest that the pieces were hand made (thinking one-at-a-time craftsman, rather than factory mass production). And to be clear, I do not want to imply that I think these were part of any furniture.
2. Saw tooth cuts. In the photo with the blue background (‘blue photo’), the teeth on the oval piece look to be cut perpendicular to the plane of the oval; whatever cut them (or filed them) was at 90 degrees. However, in the white picture, the teeth cut in to the rectangular piece appear to be cut at a slight angle as if whatever cut the teeth was not at 90 degrees. I’m guessing here, but I’d say appx 22 degrees (looks about half of 45 degrees). I also believe we’re looking at the top side of the rectangular piece as it was cut. For it to be the bottom of the piece, the cuts would angle back underneath the piece (an undercut) and that’s a very cumbersome cut to make. Think of cutting a 2x4 with a hand saw - you typically hold the handle with the saw angled towards you and it produces an angled cut. It can be held vertically to make a precise vertical cut, but to hold it away from you makes for a very difficult cut to make; much more so on such a small piece. I don’t know if this suggests more craftsman production, or that they were made by two different people/processes, or one person at different times.
3. Right handed person? I found it noteworthy that the rectangular piece might have been cut by a right handed person as the bevel in the cuts are angled off to the right (look at the center ‘V’ cut in the rectangular piece in the white picture and see how the right side of the cut is more beveled than the left side. It’s the same on the left V; the right V is harder to tell as the right side of the V is worn down quite a bit).
4. Screws and saw teeth. Both screws are in the holes closest to the teeth. In the white photo, the metal around the screw holes appear depressed as if the screws were tightened very firmly. This is more apparent in the smaller oval piece than the long rectangular piece, although both have that look. If the screws were tightened firmly, that might suggest that doing so would force the edge with the teeth to dig in to something to better hold the piece in place.
5. Wear in the non-screw holes. Both ‘non-screw holes’ (white photo) appear to be just a little smaller than the screw holes, and have some wear in the 3 and 9 o’clock position. Again, the wear appears more noticeable in the oval piece, but looks to be present in the rectangular piece as well. This suggests to me that something rubbed at 3 and 9 o’clock; laterally to the long axis of the pieces. I don’t know if we can form any conclusions from that, but it seems to me that if something actually pulled at 3 and 9 not only might it cause wear, it might well eventually place lateral stress on the piece causing it to want to pivot on the screw (hope that makes sense). The teeth biting in to whatever they were up against would resist any pivot motion, but that would be a extremely clunky way to secure the piece. That makes me think that whatever caused the 3 and 9 wear was more likely an either/or motion from one position to the other. Think of the rod often used to hold the hood of a car open - it’s either down or up and what wear it causes on the ‘pivot hole’ is most likely from one of those positions. Not suggesting a support rod arrangement, only that the wear might be from a similar ‘this or that position’. The only other way I can think of to make that wear (oval piece) would be if something like a rod was inserted into the hole and repeatedly wiggled back and forth: 3 to 9 to 3, etc., but I think that would also cause the piece to rotate around the screw.
These are just my observations. None of this gives me any clues as to what the pieces might be, how they were used, or whether this is the way they were originally made or something fabricated in the field. I’m starting to mutter to myself...