Liechtenstein, like fellow Microstate Monaco, is not listed on the Eurail list of countries. The tiny country of Liechtenstein does not have its own railway, but a railway line passes though the country, with trains operated by ÖBB (Austria’s national railway) stopping there. So yes, you can travel to Liechtenstein on a Eurail Pass.
[Rail map of Liechtenstein]
The rail system of Liechtenstein is made up of one line 9.5 km (5.9 mi) long, connecting Austria and Switzerland. This line links Feldkirch, Austria, and Buchs, Switzerland.
There are four stations in Liechtenstein:
Schaan-Vaduz (located in Schaan, also serving Vaduz)
There are only regional train services stopping at Schaan-Vaduz, are they are not regular. If you are short on time it might be quicker to go to FeldKirch and get the connecting buses to Vaduz from there. But that is a bus, not a train. We want trains. If you really want to travel by train to Liechtenstein, then check out the train schedules at the schedules at the Austrian Railways website.
There is no border control between Switzerland-Liechtenstein and Austria-Liechtenstein. If you want to get a passport stamp from Liechtenstein though, you can go to the Tourist Information Office in Vaduz, where they will stamp your passport for a small fee.