A B737 CREW ON ROLLOUT AT FLL STARTED THEIR TURN TO EXIT RWY PRIOR TO REACHING THE EXIT.

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THIS IS A DESCRIPTION OF A SERIES OF EVENTS AND ARPT FACILITIES THAT COULD HAVE LED TO A POTENTIAL RWY EXCURSION. WE WERE LNDG AT FLL WITH THE ATIS WINDS 34 DEGS AT 6 KTS; 7 MI VISIBILITY; RA; 23 CUMULO NIMBUS BROKEN; ILS RWY 27R. THERE WAS A TSTM JUST E OF JUMAR (11.3 DME ON FINAL). WE WERE FOLLOWING ACFT Y (B757) WITH MINIMUM SPACING; SO WE WERE SLOWED TO FINAL APCH SPD. AT 500 FT AGL; WE HEARD ACFT Z CHK ON TWR FREQ. TWR ADVISED HIM HE WAS 30 KTS FASTER THAN US AND APPROVED S-TURNS. ACFT Z ASKED FOR A 360 DEG TURN WHICH WAS NOT APPROVED. WE TOUCHED DOWN NORMALLY WITH THE FO FLYING. I WAS AWARE OF THE CLOSENESS OF THE ACFT Z AND ALSO THE POSITION OF THE ACFT Y B757 WHICH WAS NOW TAXIING IN ON TXWY B; JUST E OF RWY 13/31. TWR ASKED ME TO EXIT ON RWY 13/31 SIGN AND PAST IT; A WHITE RWY EDGE LIGHT. THIS WAS MY FIRST NIGHT LNDG ON RWY 27R. FROM MY EXPERIENCE; I KNEW THAT THERE WAS A WHITE RWY EDGE LIGHT IN THE MIDDLE OF HIGH SPD TURNOFF B3 (ON RWY 9L); SO I ASSUMED THAT THE WHITE LIGHT I SAW PAST THE RWY 13/31 SIGN WAS A SIMILAR SIT WITH THAT LIGHT BEING IN THE MIDDLE OF RWY 13/31. SENSING ACFT Z SHORT FINAL; I STARTED TO TURN OFF RWY 27R ONTO RWY 13/31. AS I APCHED THE EDGE; I NOTICED THE DOUBLE YELLOW LINES; INDICATING THAT I HAD NOT YET REACHED RWY 13/31. I STEERED BACK TOWARD THE CTR; WENT PAST THAT WHITE LIGHT; THEN EXITED ON RWY 13/31. MY FAMILIARITY WITH THE PRESENCE OF THE WHITE RWY 9L EDGE LIGHT IN THE MIDDLE OF TXWY B3; AND MY UNFAMILIARITY WITH RWY 27R; ALMOST LED ME TO TURN OFF EARLY FROM RWY 27R TO RWY 13/31. I SUGGEST THAT EITHER GREEN LEAD-OFF LIGHTS BE PLACED ON B3 OR THE WHITE EDGE LIGHT IN THE MIDDLE OF B3 BE REMOVED SO THAT PLTS DON'T GET LULLED INTO A SIT WHERE THEY NORMALLY TURN OFF OVER A WHITE EDGE LIGHT. CONTRIBUTING FACTORS WERE NIGHT; RAIN AND MINIMAL SEPARATION LEADING TO AN EXPEDITIOUS TURN-OFF. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: CORRECTION TO RPTR'S ORIGINAL RPT: 'TWR ASKED ME TO EXIT BEHIND DELTA; AS I SLOWED TO TURN OFF; I SAW THE RWY 13/31 SIGN AND CONTINUED PAST IT; I THEN SAW A WHITE RWY EDGE LIGHT. THIS WAS MY FIRST NIGHT LNDG ON RWY 27R....' THE RPTR STATED IT WAS RAINING; SO VISIBILITY WAS SOMEWHAT IMPAIRED. BASED ON HIS PAST EXPERIENCE LNDG ON RWY 9L WHERE B3 TURNOFF HAS A RWY EDGE LIGHT IN THE MIDDLE OF IT; HE ASSUMED THAT THE WHITE LIGHT HE SAW AFTER PASSING THE RWY 13/31 SIGN WAS THE CTR OF RWY 13/31. SEEING THE DOUBLE YELLOW LINES AT THE RWY EDGE HE CORRECTED TO THE CTR OF THE RWY; EXITING ON RWY 13/31. THE RPTR FEELS THE RWY EDGE LIGHT IN THE MIDDLE OF BE MAY LULL PLTS; IN SOME SITS; TO EXIT OVER A RWY EDGE LIGHT.