A SYS ERROR OCCURS AFTER LOSS OF SEPARATION BTWN TAXIING CE425 AND LNDG C182 AT BFI; WA.

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I WAS ACTING AS PIC AND THE PF AS PART OF A 2 PLT CREW ON A C425 CONQUEST OPERATING UNDER PART 91. THE CO-PLT WAS NAVING AND COMMUNICATING ON THIS FLT. WE APCHED RWY 13R AT BFI ON THE ILS AT APPROX 111 KIAS AIRSPACE. WE TOUCHED DOWN APPROX 1000 FT FROM THE THRESHOLD OF RWY 13R AND SLOWED TO EXIT AT TXWY A4; A HIGH SPD TXWY OFF THE L SIDE OF RWY 13R. UPON APCHING TXWY A4; WE RECEIVED SIMULTANEOUS INSTRUCTIONS FROM THE TWR TO 'EXIT AT TXWY A4; CROSS THE L AND CONTACT GND ON THE OTHER SIDE' AND AN AUDIO VOICE ANNUNCIATOR FROM OUR MODE S XPONDER WARNING US OF 'TFC.' THE PNF REPEATED WHAT WE BOTH THOUGHT WE HEARD AND I CROSSED RWY 13L AND STOPPED ON THE OTHER SIDE. WE NEVER HEARD FURTHER CORRECTIONS TO OUR READBACK TO STOP OR HOLD SHORT. WE CROSSED IN FRONT OF A CESSNA SINGLE ENG HIGH WING THAT WAS SLOWING ON ITS ROLLOUT. WE NEVER SAW THAT CESSNA UNTIL IT PASSED US. THE TWR CLAIMS THAT UPON REVIEW OF THE TAPES; WE WERE INSTRUCTED TO 'HOLD SHORT OF RWY 13L AND REMAIN ON THIS FREQ.' THE TWR ALSO CLAIMS THAT WE WERE INSTRUCTED TO STOP 3 TIMES. THIS; TOO; WAS NOT HEARD. SINCE THE SINGLE ENG CESSNA WAS SLOW ENOUGH ON ITS ROLLOUT; THERE WAS NO IMMEDIATE DANGER OF COLLISION. 2 POSSIBLE CAUSES FOR THE RWY INCURSION: 1) THE AUDIO ANNUNCIATOR PREVENTING OUR HEARING THE FIRST INSTRUCTION FROM TWR TO HOLD SHORT. 2) THE LACK OF AN IMMEDIATE CORRECTION FROM ATC AFTER OUR INCORRECT READBACK; OR NOT HEARING OTHER INSTRUCTIONS DUE TO OTHER RADIO TFC; ACFT CABIN NOISE OR AFTER LNDG CHKLISTS BEING READ. NEVERTHELESS; SITUATIONAL AWARENESS WAS LOST BECAUSE I NEVER SAW THE OTHER TFC.