AN ACR MLG WAS SLOW TO CLR A RWY INTXN.

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FO FLYING; MADE NORMAL NIGHT VISUAL APCH AND LNDG AT FLL RWY 27R. FO LANDED SLIGHTLY LONG; AND CAPT TOOK CTL OF ACFT AT ABOUT 80 KTS. WHILE SLOWING; TWR INFORMED FLT TO MAKE A L TURN TO CLR RWY. PLT KNEW HE PASSED TXWY D AND WAS ATTEMPTING TO TURN ON TXWY E (HE THOUGHT) BUT ACTUALLY STARTED TO TURN ON RWY 31 WHICH WAS BEING USED TO LAND LIGHT ACFT. THIS INTXN IS POORLY MARKED AND THE ABUNDANCE OF LIGHTS MAKE THE TXWYS HARD TO DISTINGUISH. AS THE AIRPLANE TURNED SLIGHTLY L; THE TWR RADIOED 'DON'T GO ON THE RWY.' THIS WAS A CONFUSING CALL SINCE WE WERE ALREADY ON THE RWY (27R) BUT WE REALIZED THAT WE WERE ALSO ON RWY 31 INTXN. WE CONTINUED TO GO STRAIGHT AND EXIT ON TXWY E. BECAUSE WE WERE SLOWED AND ALMOST STOPPED AT THE INTXN ON RWY 31/27R; THE TWR ISSUED A GAR TO A LIGHT AIRPLANE APCHING RWY 31. THERE WAS NO CONFLICT BECAUSE THE LIGHT ACFT WAS STILL FAR FROM THE RWY; AND WE EXITED THE INTXN QUICKLY. I DO NOT BELIEVE THE TWR WAS CONCERNED ABOUT A RWY BLOCKAGE; BUT WAS FOLLOWING STANDARD PROC. WE AT NO TIME EVER WENT DOWN RWY 31. WE JUST SLIGHTLY TURNED AND THEN WENT STRAIGHT AHEAD THROUGH THE INTXN ONTO TXWY E. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR FLIES THE B-737- 300. THE WHITE RWY LIGHTS WERE VERY BRIGHT MASKING THE BLUE TXWY LIGHTS FOR THE TURNOFF. THE ACFT DID NOT TURN ONTO THE WRONG RWY NOR DID IT STOP IN THE INTXN; BUT IT HAD SLOWED CONSIDERABLY LOOKING FOR THE TXWY. THE RPTR BELIEVES THAT THE MARKINGS ARE STANDARD; THEY WERE JUST OBSCURED BY THE BRIGHT LIGHTS. THE RPTR DOES NOT CARE MUCH FOR MULTIPLE TXWY OPS WITH XING RWYS.