I see Amtrak promoting itself on Twitter all the time, and I'm not counting Amtrak Alerts. I'm not on Facebook or Instagram, so I don't know if Amtrak's there too. I see Amtrak internet ads.
Mind you, the ads and tweets one sees are somewhat linked to what one reads/searches/clicks so that a person
could be on Twitter and the internet generally but see no Amtrak tweets or ads. However, I've also seen Amtrak billboards along the highways -- I saw one within the last couple of weeks in the vicinity of O'Hare Airport (don't remember which expressway I was on at the time) -- and there's no filter for those.
I see plenty of YouTube travel bloggers who post their Amtrak trips, and some make it clear in their videos that they get cooperation from the Amtrak marketing people.
So clearly Amtrak does advertise and market itself, just not necessarily in television ads like it's still 1978.