CTLR IS CONFUSED DURING A NIGHT OP AS TO THE LOCATION OF A PA30 WHEN TFC SIGHTED IS LOST AFTER LNDG AT TPA; FL.

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FILED IFR. SOLID IFR; RAIN; CLOUD-TO-CLOUD; LIGHTNING; TURB. ATIS SAID RWY 36L ILS AND RWY 36R LOC IN USE. APCH SAID 'CLRED FOR LOC RWY 36R. CONTACT THE TWR.' I BROKE OUT IN HVY RAIN; POOR VISIBILITY; WITH THE ADMONITION 'KEEP YOUR SPD UP; A JET BEHIND YOU.' I LANDED AND ROLLED SWIFTLY ON RWY 6R; BLUE LIGHTS WHIZZING BY. ASKED TWR 'DO YOU WANT ME TO TURN R HERE?' TWR STATED 'YES; TURN THERE.' I DID. TWR ASKED; 'WHERE ARE YOU?' I ADVISED I HAD TURNED OFF ON TXWY. TWR ASKED AGAIN 'WHERE ARE YOU?!' I REPLIED 'HDG TO FBO.' TWR SAID 'STOP AND SAY NEAREST SIGN!' I STATED 'I SEE SIGN F9/27.' TWR SAID 'YOU INCURRED AN ACTIVE RWY.' I DID NOT; BUT SAW THE SIGN IN THE DISTANCE. I TOLD TWR THAT 'YOU TOLD ME TO TURN THERE.' AFTER A LONG SILENCE; TWR STATED 'WE DIDN'T KNOW WHERE YOU WERE;' THEN MORE SILENCE. TWR THEN SAID 'PROCEED TO FBO.' (RWY 9/27 WAS NOT ON THE ATIS AS ACTIVE.) TWRS FORGET THAT SMALL PLANES LIKE A PA30; I ONLY SIT ABOUT 36 INCHES OFF THE GND; BEING HARD TO SEE IN A SEA OF LIGHTS. MAKES IT DIFFICULT FOR ALL CONCERNED WITH HVY RAIN AND POOR VISIBILITY; AND THROW IN 'KEEP YOUR SPD UP.' I FOLLOWED INSTRUCTIONS; DID AS TOLD BY TWR.