As already known, IMSI-catcher is “is a telephone eavesdropping device used for intercepting mobile phone traffic and tracking location data of mobile phone user”.
When the user registers to this fake base station, it (usually) answers with a fake location.
Can it be located nevertheless? i.E. does any device exist to do that, or is it possible to identify the real location by using some specialized software?
The SeaGlass researchers aim to find the location of IMSI-catchers via anomaly detection at a city scale: https://seaglass.cs.washington.edu/ .
To identify potential IMSI-catchers, they rely on four anomalies:
To answer your question: you may be able to detect it easily, but finding the location may require triangulation.
In addition to @crypto's answer,
if you can determine a specific transmission is from a suspected catcher, a fox hunt rig would be able to provide direction, and two of those measurements can provide a pretty small search area.
