How to wire an old single phase AC brushed motor to be reversable
Old Westinghouse Type FR motors were what is called an Induction / Repulsion motor, a very early type that is now no longer made because Capacitor Start motors are simpler and easier (and reversible). Yours probably dates back to the 1920s or 30s, maybe the 40s pre-WWII, but not younger than that. The brushes are used in acceleration only by creating repulsion with the stator windings, but are moved out of the way via a centrifugal mechanism as the motor speeds up. The video below shows the basic concept, albeit in an earlier form where the brushes were moved manually.
https://www.youtube.com/watch?v=_KdaipeodLo

The thing about those motors was, they are not reversible. Sorry.