I had these same brackets original to my house (before a rather slash and burn approach to cleaning and cosmetic updates). They can receive one of several types of rods. There is a cutout portion that acts to tension the oval shaped rod that goes between both sides. It is doubtful you will find an exact, original replacement. I suspect mind had been long lost to time and a clumsy hand.
The profile of an expandable, oval profile, curtain rode could work if you delicately cut off the curved necks (scroll saw or similar).
Similarly, it wouldn't look to out of place to whittle down a dowel rod, so that the ends were shaped and tapered to fit snugly into the brackets.