A C500 ON VISUAL APCH TO BFI OBSERVES A TFC WATCH C172 IN CLOSE PROX OPPOSITE DIRECTION. BOTH ACFT TAKE EVASIVE ACTION TO MISS EACH OTHER.

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WE WERE BEING VECTORED TO AN ILS APCH WHEN WE GOT GOOD VISUAL CONTACT WITH BOEING FIELD (OUR DEST). WE REQUESTED AND WERE GRANTED A VISUAL APCH AND WERE DIRECTED TO PROCEED TO THE SPACE NEEDLE TO INTERCEPT FINAL. NO TFC WAS CALLED OUT BY SEATTLE APCH. SHORTLY AFTER TURNING AS DIRECTED; AND DSNDING FROM OUR LAST ASSIGNED AT 2200 FT; WE NOTICED TFC SBOUND BELOW US. THEN WE NOTICED TFC HEAD ON AT OUR ALTITUDE OF 1800 FT. IT STARTED A R TURN TO AVOID AND SO DID WE. THEN SUDDENLY THE TFC TURNED SHARPLY L INTO US (EST 60 DEG BANK TURN) ON A COLLISION COURSE. THE COPLT WHO WAS THE PF EVIDENTLY MISSED THIS TURN. I GRABBED THE CTLS AND PUSHED DOWN STRONGLY TO GIVE US THE BEST CHANCE TO MISS; SINCE WE WERE ALREADY IN A DSCNT. I ESTIMATE WE MISSED BY LESS THAN 20 FT VERTLY AND LESS THAN 75 FT HORIZLY. THE OTHER ACFT WAS A C172 AND WAS A TFC SPOTTER. BOEING TWR SUBSEQUENTLY TALKED TO THE PLT WHO ADMITTED HE SAW US AND STILL TURNED INTO US WHEN HE SHOULD HAVE AVOIDED TO THE R AS PER RIGHT OF WAY RULES. I WOULD REALLY LIKE TO TALK WITH THAT PLT. THIS HAS BEEN RPTED TO OUR FAA INSPECTOR VIA MY DIRECTOR OF OPS. SUPPLEMENTAL INFO FROM ACN 371870: I RAN THE LIFEGUARD UNDERNEATH THE SEA FINAL AGAIN WITH A POINTOUT WHEN C500 SAID HE HAD THE ARPT AND WAS REQUESTING A VISUAL. WX WAS OK; BUT NOT GOOD ENOUGH TO VECTOR FOR THE VISUAL RWY 13R AT BOEING FIELD. I QUICK CHKED THE WX AT BFI AND CLRED C500 FOR THE VISUAL APCH TO RWY 13R AT BFI. I WAS ALSO RESPONSIBLE FOR FEEDING THE SEA FINAL CTLR AS OUR 4 CORNER POST SYS DICTATED. I NEEDED TO TURN A B757 TO THE DOWNWIND FOR SEA. AFTER DOING THAT I WENT RIGHT BACK TO THE LIFEGUARD AND OBSERVED A VFR DISCRETE CODE (TFC WATCH C172) UNDER THE MAZE OF DATA BLOCKS. I ATTEMPTED TO ISSUE THE TFC BUT WASN'T TIMELY ENOUGH. WE AREN'T REQUIRED TO QUICK LOOK THESE TARGETS AS THEY ARE USUALLY NEVER A FACTOR TO US AS WE ARE ALWAYS ABOVE THEM. LIFEGUARD SAID AFTER I ISSUED THE TFC THAT HE HAD JUST DODGED THAT ONE. I HAD ASKED HIM TO TURN FINAL N OF THE SPACE NEEDLE TO SPACE HIMSELF BEHIND AN AC50. HE DSNDED RAPIDLY FROM 2200 FT TO 1500 FT. THE TFC WATCH CESSNA WAS AT 1600 FT. I ASKED C500 IF HE WAS IN VFR CONDITIONS; HE REPLIED AFFIRMATIVE. ALTHOUGH I PRIDE MYSELF ON TIMELY/PERTINENT TFC CALLS; THIS ONE GOT BY ME. WORKLOAD PREVENTED ME FROM SEEING THE CESSNA IN A TIMELY MANNER. THE LIFEGUARD'S QUICK DSCNT FROM 2200 FT DIDN'T HELP. I'M SURE HE WAS TRYING TO KEEP BFI IN SIGHT CLR OF CLOUDS.