CORP ACFT CROSSES ACTIVE RWY WHEN CLRED TO HOLD SHORT.

Narrative

WAS CONDUCTING A PLT DEMONSTRATION (GIVING INSTRUCTION) TO A PROSPECTIVE BUYER OF AN ACFT WHO WAS TYPED IN TYPE BUT UNFAMILIAR WITH ALL THE TOOTS AND WHISTLES OF AN EFIS COCKPIT. HE WAS FLYING IN THE L SEAT AND I WAS CONDUCTING THE DEMONSTRATION FROM THE R SEAT. WE HAD JUST LANDED ON 35L AT LNK AND WERE CLRED TO THE RAMP; BUT TOLD TO HOLD SHORT OF 35R. I ACKNOWLEDGED THE INSTRUCTIONS AND LOOKED AT THE PLT IN THE L SEAT AND REPEATED; HOLD SHORT OF 35R. I THEN TOLD HIM I HAD MY HEAD DOWN AND IN THE COCKPIT; RECORDING SOME FLT TIMES FOR THE TRIP SHEET RECORD. WHEN I LOOKED UP AND AROUND I SAW WE WERE XING 35R WITH AN AIRPLANE ON FINAL. FORTUNATELY WE MADE IT ACROSS WITHOUT INCIDENT; BUT I WAS DUMBFOUNDED THAT THE PLT I WAS DEMONSTRATING TO DID IT. WHEN I ASKED HIM ABOUT IT HE SAID HE HADN'T HEARD THE TAXI INSTRUCTIONS; OR HEARD THEM AND THEN FORGOT THEM. IN ANY CASE I AS PIC; WITH AN INEXPERIENCED CREW MEMBER AT THE WHEEL; I SHOULD HAVE KEPT MY HEAD UP; EYES OUT OF THE COCKPIT AND LEFT THE RECORD KEEPING UNTIL THE ACFT WAS STOPPED AT THE RAMP.