When do stations move to a new location?
In the Civilization Wikia, on the Stations Page it indicates that:
Stations may land on the planet at any time. They are looking to trade with the players, and if nobody comes forward within a given period of time, they pack their belongings and move to a new location on the planet. Only one city per each civilization can trade with a given Station simultaneously.
But I haven't found anything on how much that period of time is before they leave.
Is there a confirmation of how long it takes? Also, is there a way to find out if nobody else has traded with them?
Stations will disappear after 45 turns without people sending trade routes (scaling with game speed). The game will try to maintain 2 Stations per Player, so relatively shortly after a station has withdrawn the game will try to spawn a new one (Stations CAN spawn again after they have withdrawn/been destroyed) as long as there is enough space between cities available.
Some people claim that it is 30 turns - but they may have been on different game speeds. Generally assume it is minimum of 30 and max around 45.
There is not really a way to see who is trading with them unless you are watching for trade vessels to and from the station.
Overall there is not a ton of documented information about stations mostly because of the mixed response the game got - and now with Civ VI out it has been largely abandoned.