It takes a significant amount of infrastructure in order to do HF direction finding. I believe the FCC has one facility to do it. The US military probably has a few in different parts of the globe. Egypt might have a facility or two. But the accuracy of these things will only give you city-level precision. Tracking it down further requires driving around the city with a receiver and looking at the signal strength. Not quick.
The thing with ham stations is that you don't necessarily need a big antenna on a tower or anything. You could communicate with a wire antenna in a palm tree. You could go out into the desert and raise some 10m masts. Either way, these are low-infrastructure requirements and can easily be raised and town down in a matter of an hour. It should not be difficult to relocate after every communication session, even without running mobile (on a vehicle).
Running mobile is also an option, and can be done on HF without much difficulty. A "hamstick" type antenna for the 20m band (14 MHz) is able to reach hundreds of miles, even with today's low sunspot numbers.
-molo