I removed the entire seat frame at this location. Here it is standing on end, with the broken casting removed (at the top). A test fit verified that the new casting will work just fine. But this particular seat has more than one problem. There are two arms (yellow arrows) connected to the center rod (red arrow). These arms mesh into the brackets on the seat back and should keep it straight. But one of them is bent, and the other is loose on the rod - notice that they don't line up the way they should. I will disassemble this frame and take the center rod assembly to the shop to be fixed by our metal-working experts.
These seat frames are more complicated than one might expect. The center rod has six castings attached, which rotate when the back is moved: two to keep the back straight, two to move the seat cushion, and two to move the foot rest. And the whole assembly seems to weigh slightly less than a ton!
Between a seat frame and the wall I found this little relic of Tag Day 1939. It's a piece of cardboard about 3" square. On the back it just says "Thank You". I think the missing word is probably "Charities" and that this was some sort of annual fund raiser. Does anybody remember Tag Day?