Not a pilot, but retired Licenced Engineer (mechanic) with engine run/taxi authorisation. Never had to invoke it, but consideration always made with regard to an aircraft fire, and my crew briefed accordingly. Without hesitation, it would be a Mayday to the Ground/Tower frequency in use, and worry about possible apologies afterwards. I have to add that the majority of experience is in the UK.
Incidentally, with regard to communicating the location, I think a Crash Map grid reference is ok for an incident off-piste, but you can't whack the Airfield Chart for precision. Every responder is Airfield Driving qualified (or will be so escorted) and will know exactly where "Taxiway Tango abeam Stand 23" is.