I usually do take one of my two little Magellan GPS 300 units along. They were less than $100 each when I bought them back pre-2000. They don't have maps, but I bookmark the station locations so that on succeeding trips I can get a good estimate of time and distance to the next station and so forth, and it also helps if we take a train to, say, Miami, and rent a car, It makes it much easier to find the station because although it doesn't give you maps to follow, it points to the station from wherever you are, and makes it pretty esy to find the station without having to pore over road maps while driving. I also took one or the other of those two GPS units on mission trips to the Yucatan and to Brasil, and it's kind of neat to have those Mexico and Brasil bookmarks to page through from here in Florida.
The trick in using the GPS units on the train is that you have to keep the units very close to a window pretty much, or use them in a Superliner observation lounge with that big expanse of plexiglass overhead (a single-level lounge car also works pretty well for GPS since you can put the GPS on the table right at the window, and it has a better, wider, higher "view" from there than from a regular coach), because the GPS signal won't go through metal, and unlike with cellphone towers that are basically within a couple hundred feet of the ground, or FM broadcast stations which are up to !,000 feet or so of the ground (and therefore pretty much always able to "see" you through the windows of the car), the GPS "transmitters" are satellites, and are just as likely to be directly overhead as to be near the horizon. If the skin of the rail car is between your GPS and the satellite, the GPS unit won't hear a signal from it. The GPS signal is a VERY high frequency and works like a flashlight beam - if doesn't "go around corners" or go through metal objects. You can also anticipate losing the signal from the GPS if you go through an area where a very thick forest canopy is above or close around the train (just like with a flashlight beam, thick foliage drastically attenuates the signal strength), or through a tunnel, or that sort of thing, and you may also lose tracking for a minute or two when the train makes a change in direction, because the metal skin of the train , when it changes direction of travel, frequently cuts off the signal to the satellites it had been using to track on, and it has to find new ones to track with. Also, of course, over any period of time that you are using the GPS, those satellites are constantly moving in orbit anyway, and they will pop in and out of view of the GPS as they do so, since while you are on the train you have a pretty narrow window of view for those signals.
Lastly, the GPS has to have at least 3 satellites in view in order to work out a current position, and there will be times when it only has one or two satellites in view from your train window. When that happens, it will stop updating your position until it finds and locks onto a third satellite. The GPS is an amazing piece of technology, but it does have limitations. It's much easier to use successfully when you understand how it works. Have fun with it.