DA50 FLT CREW ON ILS APCH TO ACV RPTS CONFLICT WITH OPPOSITE DIRECTION C208.

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I WAS THE PF IN VFR CONDITIONS; BUT I REQUESTED THE ILS DUE TO SCATTERED LAYER OF CUMULUS CLOUDS WITH A BASE OF 5000 FT AND TOPS TO 14000 FT. THE ASOS FOR ACV ARPT WAS RPTING CLR. I WAS ISSUED A PRIOR CLRNC TO DSND TO 10000 FT. I THEN WAS ISSUED A NEW CLRNC TO CROSS YAGER INTXN AT OR ABOVE 7000 FT; CLRED FOR THE ILS RWY 32 AT ACV. I WAS ON A R BASE TO JOIN THE LOC; BUT AT YAGER AT 28.9 DME THERE WAS A SMALL CUMULUS CLOUD WITH A TOP OF 14000 FT. I ASKED THE PNF TO REQUEST IF WE COULD TRACK L OF THE LOC (1 DOT) TO STAY IN SMOOTH AIR AND VFR CONDITIONS. AS THE LOC NEEDLE WAS COMING ALIVE I WAS IN A R BANK TO JOIN AND SKIRTING THE EDGE OF THE CUMULUS CLOUD WHILE THE PNF WAS XMITTING MY REQUEST. AT THAT POINT I THOUGHT THE CTRLINE WOULD BE L OF THE CUMULUS CLOUD; BUT I WANTED PERMISSION TO TRACK L OF THE COURSE JUST IN CASE THE CTRLINE WAS IN THE MIDDLE OF THE CLOUD. FOR THE 5 MI PRIOR TO JOINING THE LOC; MY GS INDICATOR WAS SHOWING THAT I WAS ON THE GLIDEPATH ALT. AFTER THE PNF FINISHED ASKING FOR MY REQUEST I WAS STILL IN A R TURN; BUT NOW 1 TO 1 1/2 DOT L OF THE CTRLINE PROCEEDING INBOUND. THE CTLR REPLIED BACK; 'NEGATIVE; TFC ALERT; YOU HAVE OPPOSITE DIRECTION TFC AT YOUR SAME ALT; 8200 FT.' I COULDN'T SEE THE TFC VISUALLY; BUT THEN OUR TCAS SHOWED THE TFC AS A YELLOW TA ADVISORY. I IMMEDIATELY DEPLOYED THE AIR BRAKES AND DSNDED TO OUR NEW CLRED ALT OF 6000 FT. WE THEN SAW THE TFC TO OUR R AND IT WAS APPROX ON THE CTRLINE OF THE LOC TRACKING OUTBOUND AND CLBING. I COULDN'T FIGURE OUT WHY THE CLBING TFC WAS ON THE CTRLINE OUTBOUND WHEN WE WERE CLRED INBOUND. THE CLBING TFC WAS IN VFR CONDITIONS.