Amtrak has quietly published their fare pricing system for profitable routes in a congressional report, including the NER, Acela, AutoTrain, and a few other big city links. It's the same as the big three legacy air carriers: fare buckets, just on a different demand curve based on rail passengers and not on flights. The rest of their routes are fare buckets with an artificial (sometimes government imposed) cost basis adjustment.
And since fewer Amtrak riders change or cancel than fliers, there's no magic, earlier and less flexible fares cost less and later ones cost more for any given date. If you're date flexible, check several. Since they're running so thin on equipment lately, the days of 10 years ago when they'd add rolling stock to a consist and the prices would drastically adjust down are gone.
Do check for any discounts you may qualify for though -
AARP still has one, and AAA used to (I don't believe they do anymore).
And, fun Disney fact: the WDWRR has to have its equipment periodically inspected for safety, and to do this they ship the locomotives and consists up to Amtrak's Altoona, PA, shops.