If there is no obvious corrosion through battery leakage, put a new battery in it and give it bump at the 9 o'clock position with the heal of your hand and it may burst into life. Sometimes old Accutrons need a little help to get them going.
I checked in a reference book on watch repair. The word we want is pivot. The pinion is the small part of a gear which interfaces with the teeth of a larger wheel. The "teeth" of a pinion are called its leaves. A post, in contrast to both of those, doesn't move.
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Good work Roger . Great feeling when it starts to run properly . Perseverance won the day . I was about to suggest that the hands might be hitting each other , or hitting the dial if the dial is not properly seated .