As mentioned, the saddle bit is part of the brake caliper, although you should be able to find the noodle as a spare.
Originally Posted by
Pauline
This is the type of caliper assy, where the caliper arms point upwards and are pulled together by the operation of the cable.
Enquiries at local cycle shops have proved fruitless and items found in places like Ebay, which the seller claims are SS and will not rust, do.
Brakes with hardware made of SS or plated with something that doesn't flake like chrome does are likely to be fairly high-end. I've got some 600 (Shimano's second-tier road group) brakes from the 80s here that have chromed rather than SS hardware, and it's a bummer.