B737 AT APPROX 2900 FT WITH TPA TRACON EXPERIENCED TCASII RA EVENT WITH ISSUED TFC DURING VECTORS TO RWY 18L.

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I WAS THE CAPT ON FLT. WE HAD AN NMAC WITH A C210. WE WERE APPROX 9 1/2 NM FROM RWY 18L AT APPROX 2900 FT DSNDING TO 2000 FT. OUR AIRSPD WAS APPROX 220 KIAS AND WE WERE BEING RADAR VECTORED FOR AN ILS TO RWY 18L ON APPROX A 40 DEG INTERCEPT. ATC RPTED TFC AT 11 O'CLOCK POS AND 2-3 MI AND SAID THAT THEY WERE NOT TALKING TO THEM. WE SAID THAT WE WERE LOOKING AND I TOLD THE FO THAT I HAD THE ACFT IN SIGHT AS SOON AS I SPOTTED IT. IT APPEARED TO BE A C210. IT APPEARED THAT THE C210 WAS DSNDING AND BANKING (FROM W TO N) INTO OUR ACFT; SO I DISCONNECTED THE AUTOPLT; ABRUPTLY DSNDED AND PULLED OUT THE SPD BRAKE (WHICH HELPED DSND QUICKER) TO KEEP FROM BEING IMPACTED BY THE C210. I KNEW THAT THE PLT OF THE CESSNA COULD NOT SEE US BECAUSE HE WAS IN A HIGH WING AIRPLANE. THE RA ALERTED US TO 'DSND; DSND' SECONDS AFTER I TOOK EVASIVE ACTION AND WE TOLD THE ATC CTLR WHAT WE WERE DOING AND WHAT HAD OCCURRED. OUR RECOVERY ENDED AT APPROX 1800 FT. IT WOULD HELP IF THESE GA ACFT WERE NOT ABLE TO FLY ERRATICALLY; SO CLOSE TO THE ARPT TFC OF A MAJOR ARPT. I HAD VISIONS OF THE F16 THAT RECENTLY HAD A MIDAIR AND IT WOKE ME UP AND SHOOK ME UP ENOUGH TO HOPE THAT ONE DAY ATC WILL MAKE GA ACFT MAINTAIN RADAR CONTACT IN SUCH CLOSE PROX TO MAJOR ARPTS.