4006-6089 (etc.) bracelet pin/link

Hello, long time listener first time caller here,

I picked up a poorly-cared-for 4006-6089 and the bracelet is in need of a single pin. I'm sure there is a correct term, but the pins on this bracelet are flat in a 'U' shape. I haven't the faintest idea how to go about looking since there is no part number on the bracelet. Can anyone point me in some direction, or by chance does anyone have a spare link or two to this bracelet they would be willing to part with?
Thanks!