PA31 PLT AND ANOTHER ACFT HAD A CONFLICT ON TAXI AND ON LNDG AT UNCTLED ARPT AT MYAT.

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TREASURE CAY ARPT (MYAT) IS A NON TWRED ARPT AND HAS NO TXWYS. AS I PREPARED FOR DEP; I DETERMINED THE WIND FAVORED RWY 14; SO I HAD TO BACK-TAXI THE LENGTH OF THE RWY. ON 122.8; THE CTAF; I ANNOUNCED 'TREASURE CAY TFC; CHIEFTAIN IS ABOUT TO BACK-TAXI. IS ANYONE INBOUND TO TREASURE CAY?' RECEIVING NO RESPONSE; I LOOKED BOTH WAYS FOR TFC AND THEN PROCEEDED ONTO THE RWY FOR MY BACK-TAXI. THE SUN WAS LOW IN THE SKY AND MADE IT DIFFICULT TO SEE TOWARD THE APCH END OF RWY 14. AS I ENTERED THE RWY; I ANNOUNCED ON CTAF 'TREASURE TFC CHIEFTAIN BACK-TAXIING FOR DEP ON RWY 14.' WHEN I COMPLETED MY TURN ONTO THE RWY; I SAW SOMETHING MOVE NEAR THE APCH END OF RWY 14 (THE FAR END OF THE RWY FROM MY POS); AND A PAX SHOUTED 'THERE'S ONE LNDG!' I IMMEDIATELY TURNED AROUND AND EXPEDITED OFF OF THE RWY WHILE ANNOUNCING ON CTAF 'CHIEFTAIN CLRING THE RWY AT TREASURE; ACFT LNDG ARE YOU ON FREQ?' AFTER I CLRED THE RWY THE OTHER PLANE LANDED AND I AGAIN ASKED IF HE WAS ON FREQ. HE RESPONDED BY SAYING 'YES I AM AND I ANSWERED EACH OF YOUR CALLS; DIDN'T YOU HEAR ME?' I TOLD HIM NO AND THAT I SUSPECTED HIS XMITTER HAD NOT BEEN WORKING. I THEN DEPARTED UNEVENTFULLY. I HAD CHKED MY EQUIP AFTER START-UP AND IT WAS FUNCTIONAL. NOTHING HAD HAPPENED BUT IF I HAD LOOKED HARDER BEFORE TAKING THE RWY OR IF HE HAD CHKED HIS XMITTER WE COULD HAVE AVOIDED SCARING THE PAX. AT LEAST WE SAW AND AVOIDED BEFORE IT GOT BAD.