RWY INCURSION BY A C750 FLT CREW DURING A NIGHT OP AT BPI; FL.

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THE CREW WAS INVOLVED IN A POSSIBLE RWY INCURSION. THE CREW WAS ON THE 5TH DAY OF WORK; AND HAD BEEN ON DUTY 13 HRS. THIS WAS THE THIRD DAY OF EARLY MORNING SHOWS. CREW HAD 15 HR DUTY DAY. CREW WAS IN POS ON RWY 9L FOR A TKOF FOR A FERRY TO BCT; LAST PLANNED EVENT OF DAY. PIC PERFORMED STATIC DEP. AFTER ABOUT 20 KTS; RED MASTER WARNING CHIMED AND MESSAGED APPEARED. CREW ABORTED TKOF WITHOUT INCIDENT. POSITIONED FACING W ON THE FBO AND SHUT DOWN. CREW CALLED TWR FOR CLRNC. ACFT WAS CLRED TO DO A 180 DEG TURN; AND TAXI VIA TXWY F; HOLD SHORT OF RWY 9L. THIS IS WHAT BOTH PLTS HEARD AND SIC READ BACK. WE EXECUTED THOSE INSTRUCTIONS. WHILE IN POS HOLDING SHORT ON TXWY F FOR RWY 9L; TWR READ NEXT CLRNC. THE PIC THOUGHT THE CLRNC WAS TO CROSS RWY 9L; HOLD SHORT RWY 13/31 ON TXWY F. AFTER CALLING CLR L AND ASKING IF I WAS CLR R; PIC THOUGHT SIC CLRED US; AND PIC BEGAN TAXI. AS WE APCHED CTR OF ACTIVE RWY; AN ACFT FLEW OVERHEAD. CREW HEARD ON RADIO A CALL FROM UNIDENTED ACFT 'WE JUST GOT CUT OFF; THAT WAS A DANGEROUS SIT.' AS WE CROSSED CLR; TWR ASKED WHAT WE WERE DOING. PIC EXPLAINED WHAT I THOUGHT WE WERE CLRED FOR. THAT'S ALL THE INFO THAT WAS EXCHANGED. AFTER DISCUSSIONS WITH SIC; HE DID NOT HEAR WHAT PIC HEARD. HE HEARD TWR CLR US TO TAXI DOWN RWY 13/31; HOLD SHORT OF RWY 9L. THIS INSTRUCTION MADE NO SENSE TO ME AS WE WERE POSITIONED ON TXWY F HOLD SHORT OF RWY 9L. IT WOULD BE ALMOST IMPOSSIBLE TO COMPLETE A 180 DEG TURN OUT OF THAT POS AT NIGHT WITHOUT XING THE HOLD SHORT LINE AND GO BACK. THE NEXT LOGICAL INSTRUCTION FOR US WOULD BE TO CROSS RWY 9L. I BELIEVE THAT MULTIPLE FACTORS PLAYED A ROLE IN THIS. ATC DID NOT KNOW ACFT WAS POSITIONED AT TXWY F HOLD SHORT OF RWY 9L. CREW PIC MISUNDERSTOOD INSTRUCTIONS. CREW SIC DID NOT USE SAFETY OF FLT OVERRIDE CAPABILITY AND STOP ACFT FROM MOVING WITH BRAKES OR VERBAL COM. THE RECENT ABORT LED TO POSSIBLE DISTR OF CREW. AFTER 13 HRS OF DUTY; WITH A PREVIOUS DAY OF 15 HRS; CREW WAS OPERATING ON REDUCED REST FROM A BRIEF WAKE-UP; FATIGUE WAS SETTING IN. SUPPLEMENTAL INFO FROM ACN 608967: WE PROCEEDED W ON TXWY C SINCE WE ADVISED TWR AND WERE CLRED TO LINE UP FOR TKOF AGAIN. THE CAPT INSTRUCTED ME TO CALL TWR AND ADVISE THEM WE NEEDED A FEW MINS BEFORE WE WERE READY. THE CAPT THEN CALLED OUR COMPANY TO ADVISE THEM OF OUR SIT. OUR COMPANY INSTRUCTED US TO TAXI BACK TO THE FBO AND CALL IT A NIGHT. ONCE IN POS AT TXWY F HOLDING SHORT OF RWY 9L; TWR REQUESTED US TO BACK TAXI RWY 13/31 AND HOLD SHORT RWY 9L. I READ THE CLRNC BACK TO TWR; AND WAS SOMEWHAT CONFUSED TO WHAT HE WANTED US TO DO. THE CAPT THEN TAXIED ACROSS RWY 9L AND THE ACFT THAT WAS ON APCH TO RWY 9L EXECUTED A GAR. I BELIEVE THAT TWR WAS UNAWARE OF OUR POS FROM THE LAST CLRNC HE HAD GIVEN US; WHICH BROUGHT CONFUSION ON OUR PART. WE SHOULD HAVE CLARIFIED WHAT THE TWR WANTED US TO DO BEFORE MOVING THE ACFT. AS CREW MEMBERS; OUR COM SHOULD HAVE BEEN BETTER BTWN US TO DISCUSS WHAT THE TAXI INSTRUCTIONS WERE INSTEAD OF ACTING UPON NOT WHAT WAS CLRED.