RWY INCURSION RESULTS IN A GROUND CONFLICT AT A NON-TOWER ARPT WHEN A CORPORATE JET CROSSES AN ACTIVE RWY.

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I STARTED THE ENGINES AS A RATED PLT; PF; L SEAT; IN ACCORDANCE WITH COMPANY SOP. I WAS LISTED AS SIC FOR THE FLT. THE PIC; PNF; WAS IN THE R SEAT. HE ANNOUNCED OUR INTENT TO TAXI TO RWY 28 FOR DEP. PREVAILING WIND WAS RPTED AS 220/08. KTRK HAS 2 RWYS; 10/28 - 7000 FT AND 01/19 - 4650 FT. AS WE CLRED THE MAIN RAMP AREA; I CALLED FOR THE TAXI/BEFORE TKOF CHECK LIST. WE; AS A CREW; BEGAN RUNNING THE CHECK LIST. AS WE APCHED THE INTERSECTION OF 01/19; WHICH IS APPROX 3000 FT FROM THE THRESHOLD OF RWY 19; I LOOKED TO CLEAR RWY 19 AND SAW NOTHING. I THEN LOOKED TO CLEAR RWY 01 AFTER WHICH I WAS DISTRACTED BY A COMMENT BY THE PIC. I DID NOT LOOK BACK TO RWY 19; NOR DID I ANNOUNCE THE RWY 'CLEAR'; AS WE CROSSED THE INTERSECTION. AT APPROX THAT TIME THE PIC STATED HE WAS GOING TO OAKLAND CTR TO GET OUR IFR CLRANCE. AT SOME POINT; HE SWITCHED FROM UNICOM TO CTR FREQ ON THE #1 RADIO; WHICH I HAD BEEN MONITORING. WHEN HE CALLED; 'MONITOR #2 RADIO FOR UNICOM'; WE WERE THROUGH THE INTERSECTION AND ON THE TXWY TO RWY 28. I THEN HEARD OUR TAIL # ON THE UNICOM AND A PLT ASSERTING THAT THERE HAD BEEN A 'NEAR COLLISION.' I LOOKED BACK; AS BEST MY FIELD OF VIEW WOULD ALLOW; BUT STILL DID NOT SEE HIM. HE WAS ALSO DEMANDING THE NAME OF THE PIC. AFTER THE PIC HAD RECEIVED THE IFR CLEARANCE; HE REJOINED ME IN MONITORING THE UNICOM FREQ. I EXPLAINED WHAT WAS SAID AND THE REQUEST FROM THE OTHER PLT. THE PIC REPLIED THAT HE WOULD NOT REVEAL HIS NAME; AS PER COMPANY POLICY. THE OTHER PILOT WAS BELLIGERENT AND AFTER THE PIC'S REFUSAL TO GIVE HIS NAME; THREATENED FAR ACTION. THE PIC THEN QUESTIONED ME AS TO WHAT I SAW. I TOLD HIM I HAD LOOKED BOTH WAYS AND SAW NOTHING. THE PIC HAD BEEN 'HEADS DOWN' IN THE COCKPIT DURING THE APCH AND CROSSING OF THE 01/19 INTERSECTION. AFTER WE LEVELED IN CRUISE FLT; THE PIC ASKED OUR FLT ATTENDANT; WHO IS ALSO COMMERCIAL/INST PLT; IF HE SAW ANYTHING. HE SAID HE SAW A C172 ON RWY 19 MOVING AT 'TAXI SPEED OR LESS.' THE PIC THEN ASKED IF THE C172 HAD USED ANY EVASIVE ACTON OR UNUSUALLY HARD BRAKING? HE RESPONDED 'NO'; AND THAT IT LOOKED AS IF HE WAS TAXIING AND WOULD GO BEHIND US TO TAKE THE TXWY THAT WE WERE VACATING. HE SAID HE DIDN'T THINK ANYTHING OF IT. IN FACT; HE DIDN'T MENTION IT UNTIL QUESTIONED BY THE PIC; SINCE HE THOUGHT EVERYTHING LOOKED 'NORMAL.' THE PIC THEN QUESTIONED HIM AS TO THE DISTANCE BETWEEN EACH ACFT AS WE CROSSED THE INTERSECTION; TO WHICH HE ESTIMATED 300 FT. THE SITUATION; AS DESCRIBED ABOVE; OBVIOUSLY EVOLVED FROM MY FAILURE TO SEE THE OTHER ACFT. CONTRIBUTING FACTORS THAT DEVELOPED AFTER A CREW DISCUSSION; WERE AS FOLLOWS: HIGH WORK LOAD IMMEDIATELY AFTER STARTING THE TAXI. MULTIPLE RWYS IN USE; DUE TO MIX OF LIGHT SINGLE ENG. ACFT AND OUR JET; WHICH REQUIRED THE LONGER RWY TO MEET PERFORMANCE CRITERIA. IT IS NOT KNOWN IF ALL ACFT WERE UTILIZING THE UNICOM FREQ; TO FULL ADVANTAGE; SINCE NEITHER OF US REMEMBERS HEARING THE C172 ON FINAL FOR RWY 19. WE HAD CROSSED 13 TIME ZONES IN 3 DAYS. ALTHOUGH WE HAD PROPER REST THE NIGHT BEFORE; AND I AWOKE FEELING WELL AND RESTED; WERE WE AT OUR BEST? WAS OUR SITUATIONAL AWARENESS AT 100%? THE PASSENGER ON THIS LEG WAS EARLY AND WANTED TO GET GOING. DID THIS ADD TO DISTRACTIONS AND CAUSE US TO RUSH? THE PIC RELIED ON ME TOTALLY TO CLEAR THE RWY AND WAS HEADS DOWN WHEN THE INTERSECTION WAS CROSSED. CORRECTIVE ACTIONS TO AVOID A LIKE SITUATION IN THE FUTURE ARE AS FOLLOWS: STRICT COCKPIT POLICY AND PROCEDURES FOR UNCONTROLLED ARPTS-- CLEAR ANNOUNCEMENT BY THE PF ON AN IMPENDING RWY CROSSING; WHICH WOULD ALERT BOTH PLTS TO 'CLEAR' THE RWYS. MAKE AN ADVISORY CALL-OUT ON UNICOM OF AN IMPENDING RWY CROSSING. MAINTAIN UNICOM WATCH ON #1 RADIO ONLY; WITH THE #2 RADIO FOR CLRNC. DEL;AWOS;FBO;ETC. NEVER ALLOW THE 'INSIDE' WORKLOAD TO OVERRIDE 'OUTSIDE VIGILANCE.' BE AWARE OF AFFECTS THAT CROSSING MULTIPLE TIME ZONES CAN HAVE ON ONE'S BODY CLOCK; CONTRIBUTING TO A LESSENED SITUATIONAL AWARENESS. SUPPLEMENTAL INFO FROM ACN 493105: I ASKED MY FO IF HE SAW THE OTHER ACFT AS WE TAXIED AND HE SAID 'NO.' HE LOOKED BOTH WAYS AND SAW NOTHING SO HE CONTINUED TO TAXI ACROSS 01/19 AS I CONTINUED THE CHECK LIST. I WAS NEVER PROMPTED TO HELP CLR THE INTERSECTING RWY HENCE I NEVER DIVERTED FULL ATTENTION 'OUTSIDE' THE ACFT. CORRECTIVE ACTIONS: FOREMOST WOULD BE TO HAVE STRICT COCKPIT POLICY AND PROCEDURE TO HAVE IT CLEARLY STATED WITHIN THE COCKPIT OF IMPENDING RWY CROSSING. THIS WOULD CUE ALL PLTS TO BE 'OUTSIDE' THE COCKPIT. MAKE RADIO CALL ADVISING ANY TFC THAT WE WOULD BE CROSSING A RWY. NEVER ALLOW 'INSIDE' WORKLOAD TO OVERRIDE OUTSIDE VIGILANCE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THAT HE BELIEVES THAT CUMULATIVE FATIGUE RESULTED FROM CROSSING MANY TIME ZONES WITHIN THREE BUSY DAYS. THIS LED TO THE SUBSEQUENT BREAKDOWN IN COCKPIT COORDINATION AS EVIDENCED BY THE NON-FLYING PLT WHO INADVERTENTLY SWITCHED THE NUMBER ONE RADIO OFF CTAF; AND FAILING TO ASSIST IN TFC WATCH DUTIES.