How does direction finding work when using GMS mobile station and additional handset?
The fact that this thing only has a single antenna port and a loudness knob:

This will just look for a transmitter in the band of interest, and you'll have to turn around a directive antenna until the tone gets loud. 

That's absolutely low-tech, it can't discern between GSM phones logged into the same network (and also active), and the whole setup will only work if the straightest path to the phone is also the one that delivers the most energy – which is not the case for e.g. a lot of the indoor and urban mobile channel scenarios that we use nowadays.