Fair question. Not a contester here & don't play one on TV, less a few very short CW events or the occasional cross-band military event once in a blue moon. (These folks will publish well in advance what they're transmitting on & their listening freq).
The short of it is that it's the calling station's decision, assuming he can make it work on both frequencies; and apparently they don't give that alot of consideration either. The most common thing I've heard from a DX station (OCONUS) is "listening up five", so
for example he is transmitting on 14.295, therefore listening on 14.300, which makes everyone pile up their signals on an internationally acknowledged emergency frequency center point.
From what I can tell the biggest difficulties from originating stations, especially those who are quite far away from their listening freq, is that they seldom identify, which should include the above notification. They get on one time and then just keep saying QRZ so, as you say, hunting them down can be tough.
Seems these days if someone isn't "spotting" on the internet no one knows who they're talking to. You can hear stations getting their standard '59' signal report and then asking the DX station, "your CALL, please give me your CALL."
There might be some more secret-squirrel etiquette involved in one of the DX "How to" guides online or from DXCC or DXZone.
Good luck with all that.
