'65 Formula S Power Brake Booster Problem

That's a Bendix booster which doesn't have your traditional later style diaphragm. It has two pistons and a ring type setup with the ring having a leather seal. There's also in internal poppet diaphragm which is more like a gasket. There are 3 internal springs and a couple more seals. It also uses an external vacuum hose and an air filter. This design was fairly trouble prone compared with the later Kelsey Hayes and Midland boosters. Unless you really need to have boosted brakes, I'd recommend going to manual brakes. Using the right parts, it doesn't take much more effort to stop the car and gives much better feel.......and one less thing to go bad. It also gives you a lot more room on the driver's side to do repair work.