Upvote:4
Amsnag is what you want.
Note that for most Amtrak routes, especially the long distance ones, the base fares are relatively static from one day to the next - they will go up over time though as the cheapest tickets sell out. However the cost of bedroom accommodation can be 50% or even 100% higher from one day to another.
On the commuter routes such as the NE corridor there will be variation on fares throughout the day (and between train types).