I'm unable to answer your question as to what the copper part actually is. My guess is the motor may be a repulsion start/induction run motor, and that copper part may be part of a contactor mechanism which cuts out the starting (replusion) windings when the motor reaches operating speed.
As to obtaining another replacement part, it may as well be unobtainium. You very likely have the means to make more of them right at hand. Namely: the part is flat copper. Mike it, get some copper of equal thickness (or thicker and take it down to required thickness using a coarse bastard file and rubbing on emery cloth). Then, lay out the part on the copper, cut to shape using anything handy: bandsaw, hacksaw, drills, and files. Hand files, a hacksaw, and a vise are about all you'd need aside from the chunk of copper plate. You have the actual part to use as a template. You will "find" more of them in your shop, lurking inside a piece of copper plate, waiting to be cut and filed to release them from inside that copper plate. Kind of like the sculptor who, when asked how he produced a statue from a chunk of stone replied: "I look at the stone and chip away anything that does not look like the statue I want to create". Files, vise, and your hands and eye are about it. Drilled holes to end a slot, hacksaw cuts to rough it out, and patience with the file will do it.
