Ok. Going to catch the TE in April and spend a week in LA up in Hollywood. To me the train and then LA is two vacations in one.
The TE is an even more complicated case than the LSL! The Eagle runs daily to San Antonio (and the reverse), but 3 days a week, it meets up with the west-bound Sunset Limited, which left New Orleans that morning. Both the SL (train 1) and the TE (train 21) arrive in SAS in the evening and two cars (a sleeper and a coach, and maybe the cafe?) join up with the west-bound SL, which departs early the next morning for LA. When you are reserving tickets, you might see options for 1, 21 and 221, depending on which car you are riding in. Beware of split tickets (part way in 21, part way in 1, for example) because that means you'll have to change cars or rooms in the middle of the night! To make it even more confusing, during busy times of the year, the TE has an extra coach from CHI to Saint Louis, which it drops off there. This is in the ticketing system as train 421! If you are booking tickets between two points west of San Antonio, you might see two choices, either 1 or 21. These are both on the same train!
East-bound the 2/22 splits in San Antonio, with the 1 part continuing to NOL and the 22 continuing North to CHI.
The 21 arrives in SAS about 10:15 on the second night, but doesn't leave until about 4 or 5 AM. (I don't know; I've always been sound asleep!) Anyway, it's at least an hour after the 1 arrives at 2:45 AM (if on time). If the TE isn't too late, you have plenty of time to take a long walk (the River Walk is a few blocks from the station) and get a late dinner at one of the dozens of restaurants in the area. Also visit the Alamo, which will be closed, but you can see the outside! Lots of people have warned that if you don't get back to the station in time, they will make you wait outside until they start boarding the 1, in the wee hours of the morning, but this has never been an issue for me. Either I got back before they closed the train, or if they see you approaching and recognize you as a passenger, they'll let you back on. Or maybe this is one of those "It's Amtrak, Jake" situations and it entirely depends on the crew. At least once, the sleeper and coach were sitting by themselves (no engine) on the track near the station. There was power, so they must have had it plugged in to a power supply on the platform.
This is one of the fun things about Amtrak, it is always an adventure, even when things are working perfectly!