There is a lot that is left to be published online regarding rod brakes. They are relatively simple devices, so maintenance is not that difficult.
Some of the best advice we’ve ever found about rod brakes is contained in a short section of a very handy bicycle repair book:
Stirrup and Other Rod-Operated Brakes
Stirrup brakes are still used on some traditional English bikes, as well as in much of the Third World. They are not operated by cables but by means of pull rods that connect the lever via a series of frame-mounted pivots to the brake arms, which are pulled radially in towards the inside of the rim. In some other parts of the world, you may find drum brakes operated the same way.Stirrup brakes and other rod-operated brakes are usually adjusted by means of a knurled round nut or a screw at the end of the rod where it is attached to the stirrup or the drum brake’s activating lever. Apart from the usual brake pad maintenance, they should be lubricated at the pivot points once a month, at the same time each of the attachment nuts should be tightened. Straighten any bent rods and your rod-operated brakes will work forever.
-Robert Van der Plas, pg. 126, The Bicycle Repair Book
As far as which oil to use, we prefer a tiny drop of Boeshield T-9.
In January of 2012, we published a short video and article about restoring the rod brakes on an old Raleigh roadster. You can see the video below:
