MD83 FLC INITIATE TCASII MANEUVER DUE TO UNIDENTED TFC WHILE ON RSW VECTOR.

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ON VECTORS FROM RSW; WE WERE ON A VECTOR OF 160 DEGS LEVEL AT 5000 FT. APCH WAS VECTORING TFC ON RWY 24 AND ONLY 1 CTLR WAS PRESENT AND FORGOT ABOUT US. WE HAD BEEN GIVEN TFC AT 1 O'CLOCK POS AT 4500 FT; HOWEVER; THERE WAS A SCATTERED LAYER AND THAT IS WHEN WE SHOWED TFC AT 12 O'CLOCK POS AND WAS CLBING TO OUR ALT OF 5000 FT. WE WERE UNABLE TO NOTIFY ATC BECAUSE OF HIS WORKLOAD. THE FO NOTICED THAT THE OTHER VFR TFC WAS GETTING CLOSER AT OUR ALT AND THEN THE TA WAS ANNOUNCED FOLLOWED BY AN RA. I CLBED UP TO 6000 FT AND OUT OF 5700 FT WE WERE GIVEN A CLR OF TFC BY TCASII. AT 6000 FT WE WERE ABLE TO FIND A BREAK IN THE FREQ AND NOTIFIED ATC THAT WE HAD AN RA. ATC WAS SURPRISED BECAUSE THE TFC WAS AT VFR ALT. WE THEN DSNDED TO 5000 FT AND WERE GIVEN VECTORS TO THE ARPT. I LATER CALLED THE APCH FACILITY AND TALKED WITH SUPVR. THEY DID PULL THE TAPES AND FOUND THAT THE CTLR FORGOT ABOUT US AND I DID MENTION THAT WE NEVER DID SEE THE TFC BECAUSE OF THE SCATTERED CLOUDS. EVEN THOUGH THE TFC WAS SUPPOSED TO BE AT A VFR ALT AND CLR OF CLOUDS; IT DIDN'T BRING ANY SURPRISE TO THE CTLR'S ATTN. HE SAID THAT IS NOT UNCOMMON. THE CTLR WAS VERY POLITE AND INVITED US TO THEIR FACILITY WHEN WE GOT A CHANCE. THE CALL WAS APPRECIATED. SUPPLEMENTAL INFO FROM ACN 505001: THE CONTRIBUTING FACTORS WERE THAT RSW WAS RUNNING 2 ARR CORRIDORS AND WAS PREOCCUPIED WITH THE E SIDE CORRIDOR; AND FAILED TO NOTICE THE CONFLICT. ALSO; THE VFR TFC WAS NOT TALKING TO ANYONE WHILE MAINTAINING AN IFR ALT. THE TCASII WAS OUR ONLY WARNING TO THIS CONFLICT DUE TO THE HAZY CONDITIONS AND A SCATTERED LAYER BTWN 4000-6000 FT.