B737-300 DSCNT TO OCCUPIED ALT. TCASII RA SENDS HIM INTO EVASIVE ACTION CLB DSCNT. ALT OVERSHOOT IN DSCNT.

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THE DEV OCCURRED AT THE END OF THE TOTAL SCENARIO THAT LASTED APPROX 20-30 SECONDS. FIRST; I WAS IN AN IDLE DSCNT; LNAV; LEVEL CHANGE AND AUTOPLT ON TO AN ALT OF 15000 FT MSL. AS I WAS DSNDING THROUGH APPROX 16000-16300 FT MSL; I HAD A 'TFC; TFC;' TCASII AND I THEN WENT TO A VERT SPD OF ABOUT 1000-1500 FPM TO KEEP FROM GETTING AN RA BUT AT ABOUT 15300 FT MSL I RECEIVED A 'CLB; CLB; CLB;' TCASII RA. I THEN DISCONNECTED THE AUTOPLT AND FOLLOWED THE TCASII RA TO APPROX 15800-16200 FT WHEN TCASII SAID 'MONITOR VERT SPD.' I THEN STOPPED MY ASCENT AND STARTED BACK DOWN TO 15000 FT MSL ASSIGNED BECAUSE I WAS AT APPROX 15800-16200 FT. SECOND; THE RA WAS COMPLIED WITH ADHERENCE TO SOP AND COMPLETED WHEN TCASII SAID 'CLR OF CONFLICT.' I WAS NOW DSNDING THROUGH APPROX 16200 FT TO 15000 FT WITH THE AUTOPLT OFF. AS I AM APCHING 15000 FT FOR THE SECOND TIME; THE TCASII SAYS 'TFC; TFC;' AGAIN WITH THE SAME TARGET TO MY R WHICH IS N OF MY POS. BECAUSE IT WAS VMC; I FELT A BIG DESIRE TO ACQUIRE THE TFC VISUALLY AND I DID SEE THE BRASILIA ACFT. I THEN STATED TO THE CAPT 'I HAVE THE ACFT IN SIGHT; NO FACTOR.' THIS ALL HAPPENED AT ONCE AND I WAS VISUALLY FIXATED ON THE ACFT FOR A MOMENT OF TIME AND DSNDED THROUGH MY ALT. AS WE CAUGHT OUR OWN DEV; I IMMEDIATELY WENT BACK TO 15000 FT. IN CLOSING; THIS EVENT TOOK APPROX 20-30 SECONDS FROM BEGINNING TO END. THE HUMAN FACTORS WORKLOAD TASKING WAS VERY HIGH AND INTENSE WITH ANOTHER ACFT IN THE AREA. ACQUIRING THE ACFT VISUALLY WAS A RELIEF AND AN IMPORTANT TASK AT THE PARTICULAR MOMENT IN TIME. THE SIT WAS TOO DYNAMIC AND SHORT TO COME UP WITH A QUICK SOLUTION TO THIS SIT.