I kept that article for quite a while, it was from 1972 or 1973.
I did the work to a pair of Mafac racer brakes long ago, here are the basics:
Start with clean parts, use some fine files (a selection single cut) to get rid of the casting marks. On the Mafacs some of these were quite big, one had to plan where the final surface would end up. Move to emery cloth to smooth the surfaces, then to the fine stuff to start the burnishing, I used wet/dry at this point with water, (and a little soap as a wetting agent) ending with 400 grit. 000 steel wool to finish prior to wax taking care to plan the direction of burnish to assist the aesthetics. Big time work, I used, but not mentioned in the article a jewelers vise, made of wood with leather faces and tensioned with a wood wedge to hold the parts, it made the work much easier than trying to brace a brake arm in ones own hand, hands cramp too fast.
Time investment, three hours for the first one including reassembly. When one is done it is apparent the lack of time in the polishing and plating of the fasteners.
The finish also needs upkeep, if I had time and $ back then I would have taken the parts to be anodized.
John Jorgensen
Palos Verdes Ca