FLC OF A BEECH 1900C AIRLINER (BE02); STARTED TAXIING ONTO RWY FOR AN IFR DEP AFTER ANNOUNCING ON TWR FREQ (TWR CLOSED) THEIR INTENTIONS WHEN SUDDENLY SIGHTED A LIGHT TWIN DEPARTING TOWARD THEM FROM THE OTHER END OF THE RWY. THEY IMMEDIATELY STOPPED PAST THE HOLD SHORT LINE AND THE OTHER ACFT PASSED OVERHEAD AFTER TKOF.

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NO RPTED TFC IN THE KEY WEST AREA ON UNICOM CTAF 118.2. THE WIND APPEARED TO BE DIRECTLY OUT OF THE N 360 DEGS AND THE RWY DIRECTION IS 9-27 DEGS. I THEN CONTACTED NAVY APCH TO OBTAIN AN IFR CLRNC TO MIAMI. I RECEIVED AN IFR CLRNC AND VOID TIME. I TOLD NAVY APCH WIND APPEARED 360 DEGS AND PREFERRED RWY 9. WHILE TAXI FROM THE TERMINAL TO RWY 9 WE CALLED ON 118.2 AND REQUESTED AIR TA'S. NO RESPONSES WERE HEARD SO WE DID OUR FINAL CHKS AND BEGAN TAXIING OVER THE HOLD SHORT LINE. WHILE TAXIING OVER THE HOLD SHORT LINE MY FO OBSERVED TFC DEPARTING ON RWY 27. WE IMMEDIATELY STOPPED AND TRIED TO ESTABLISH COM WITH THE DEPARTING TFC AND NO ANSWER WAS HEARD. WE THEN CALLED FOR TA'S AND THE PATTERN WAS CLR SO WE DEPARTED RWY 9. I FEEL THE SIT COULD HAVE BEEN AVOIDED BY BETTER POSITIONING MYSELF ON THE TXWY IN FRONT OF THE HOLD SHORT LINE SO THAT BOTH THE FINAL APCH AND RWY ARE DISTINCTLY VISIBLE TO BOTH PLTS. IN A NON RADAR ENVIRONMENT; I FEEL THAT WE SHOULD HAVE BEEN MORE PERSISTENT IN TRYING TO ESTABLISH COM WITH THE OTHER ACFT.