A LOW TIME CESSNA PLT WAS CLRED ACROSS AN ACTIVE RWY; BUT BECAME CONFUSED AND TURNED ONTO THE RWY INSTEAD. THE CTLR DID NOT OBSERVE THE RWY INCURSION AND CLRED A GULFSTREAM ACFT FOR TKOF WITH THE CESSNA ACFT TAXIING APPROX 1 MI DOWNFIELD. THE CTLR CITES HVY WORKLOAD AND FREQ CONGESTION AS A REASON FOR NOT DETECTING THE CESSNA.

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I WAS WORKING LCL CTL AT BFI. GND CTL REQUESTED TO CROSS THE CESSNA AT THE DEP END RWY 31L. I APPROVED IT. THIS WAS A NONSTANDARD OP DUE TO THE MAIN TXWY ON THE ARPT BEING CLOSED FOR CONSTRUCTION DURING OUR BUSIEST PERIOD OF THE YEAR. THE PLT OF THE CESSNA; 80 HRS TOTAL FLYING TIME; TURNED ONTO THE RWY INSTEAD OF XING IT AS INSTRUCTED. THE PLT OBSERVED A JET TURNING ONTO THE RWY APPROX 1 MI AWAY. HE MOVED OVER TO THE EDGE OF THE RWY; BUT NEVER SAID ANYTHING. THE COLOR OF THE ACFT AND HIS POS WAS SUCH THAT HE BLENDED IN WITH THE RWY PAINT. I CLRED THE GULFSTREAM FOR TKOF; THEN OBSERVED THE CESSNA JUST PRIOR TO THE GULFSTREAM ROTATING. AFTER THE JET PASSED OVER THE CESSNA; THE CESSNA ASKED GND CTL IF HE WAS IN THE RIGHT PLACE. CURRENTLY; THIS HAS NOT BEEN CLASSIFIED AS A PLTDEV. I FEEL 2 MAJOR FACTORS PLAYED INTO THIS EVENT. CTLR WORKLOAD AND FREQ CONGESTION WERE GREATLY INCREASED (BOTH LCL AND GND) WITH THE ONLY TXWY ON THE E SIDE OF THE RWY CLOSED FOR CONSTRUCTION AT MID FIELD. SECONDLY; THE ACFT OUT OF THE FBO THAT THE CESSNA IS BASED OUT OF ARE CONTINUALLY DIFFICULT FOR THE TWR TO WORK -- OFTEN NOT FAMILIAR WITH LCL AIRSPACE AND PROCS. THE PLT IN QUESTION SAID HE DID NOT KNOW THERE WAS A W SIDE TXWY. INSTEAD OF QUESTIONING; HE USED THE RWY.