AN EMB120 FLT CREW EXPERIENCES A TCASII AND HAD AN NMAC.

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WE WERE CLBING FROM 7000-12000 ON A VECTOR FOR THE LOS ANGELES GORMAN 3 DEP ON A FLT FROM LAX TO BFL. AT ABOUT 8600 FT MSL OUR TCASII ALERTED US TO TFC AT 1 O'CLOCK POS; 2 MI; PLUS 200 FT. AS WE ACQUIRED THE TARGET VISUALLY; SOCAL APCH NOTIFIED US OF THE VFR TFC; A CESSNA 421 GOLDEN EAGLE. I TOLD SOCAL THAT WE HAD THE TFC IN SIGHT AND ASKED TO WHAT ALT THEY WERE CLBING. SOCAL ASKED THE CESSNA; WHO RESPONDED '12500 FT.' OVER THE NEXT FEW SECONDS; IT BECAME APPARENT THAT WE WERE ON A COLLISION COURSE WITH THE CESSNA. AT ABOUT 9000 FT; MY FO; THE PF; INITIATED A DSCNT; AND THE CESSNA FLEW DIRECTLY OVERHEAD. THE TARGET'S ALT ON THE TCASII VARIED BTWN +100 TO +200 AS IT FLEW OVER US. AFTER THE CESSNA PASSED; SOCAL TOLD US TO CLB TO 10000 FT; AND THAT WOULD BE THE FINAL. HOWEVER; NO OTHER MENTION OF THE CESSNA TFC WAS MADE BESIDES THE INITIAL CALL. WE WERE NEVER ASKED TO MAINTAIN VISUAL WITH THE TFC IN OUR CLB. I FEEL THAT SINCE WE WERE BOTH TALKING TO SOCAL; THAT ONE OF US SHOULD HAVE BEEN TOLD TO STOP OUR CLB UNTIL WE PASSED EACH OTHER. I BELIEVE THAT IF WE HAD NOT TAKEN EVASIVE ACTION; WE WOULD HAVE HIT THE CESSNA IN A MID-AIR COLLISION.