Gambit,
Air ambulances in the US have the letters LN in for the first two letters of their call sign. Like you guys medivac aircraft get priority handling, basically we short cut their routes when possible, and make them first in the approach/departure sequence.
What I discovered was that some pilots that were only deadheading were still using their Life Guard call signs which afforded them prioity when they didn't need it, so I started asking the pilots what the nature of their patient was (critical, organ transfer, medical transfer, or dead heading home, etc.).
If the aircraft was dead heading I would put a remark in the flight plan "No Patient on board", or if it was an Organ transfer which is time critical I would put "Critical Organ transfer", or "Critical Patient on board" so that controllers down the road would know what level of priority to afford the aircraft.
I've seen controllers at Atlanta and Chicago give medivac/air ambulances direct to the initial arrival fix in front of all the other arrivals, and I've seen enroute facilities coordinate flights through restricted areas because a critical patient was on board and the aircraft needed to get to their destination as fast as possible, and I've pulled aircraft out of the arrival sequence to squeeze in a medivac/air ambulance flight.