A LNDG B737-300 FLT TAXIES OFF RWY 27 PRIOR TO THE DESIRED TXWY B8; USING THE OVAL CEMENTED AREA THAT WAS NOT WELL DEFINED AT SAN; CA.

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FLT FROM EWR-JAN. A B737-800. DURING THE APCH BRIEFING; WE (CAPT AND FO) NOTED FROM THE ATIS THAT TXWY B7 WAS CLOSED DUE TO CONSTRUCTION. WE PLANNED ON EXITING RWY 27 AT TXWY B6 (AS I DID THE PREVIOUS EVENING ON THE SAME FLT). AFTER LNDG ON RWY 27 SAN; LINDBERGH TWR REQUESTED FLT TO EXPEDITE CLR OF RWY 27 VIA TXWY B8. AT THE END OF RWY TXWY B8; MARKINGS WERE NOT CLR -- POSSIBLY DUE TO CONSTRUCTION IN THE AREA. WE EXITED RWY 27; JUST PRIOR TO TXWY B8; ON THE OVAL BTWN TXWYS B7 AND B8 IN A CLR; DRY UNOBSTRUCTED AREA; NOT IN THE CONSTRUCTION SITE. GND CTL INFORMED US THAT WE WERE THE SECOND CONVECTIVE FLT THAT EXITED THE RWY IN THE SAME EXACT LOCATION. WE TAXIED SLOWLY AND CAREFULLY -- CLR OF ALL OBJECTS. AT THE GATE; WE REQUESTED THE CTL TWR'S TELEPHONE NUMBER. I CONTACTED LINDBERGH TWR VIA TELEPHONE AND DESCRIBED THE INCIDENT. THEY SUGGESTED THAT I CONTACT THE ARPT SUPVR. I LEFT A MESSAGE AND CONTACTED A SAN DIEGO AGENT SUPVR THE FOLLOWING MORNING. I ADVISED HIM THAT TXWY B8 AREA WAS NOT CLRLY MARKED OR WELL LIT. I OFFERED THE FOLLOWING SUGGESTIONS TO PREVENT SIMILAR OCCURRENCES: 1) IMPROVE TXWY B8 MARKINGS. 2) INSTALL RWY TURNING LIGHTS AND/OR RED LIGHTS AROUND THE OVAL NEAR THE CONSTRUCTION SITE. HE AGREED WITH THE SUGGESTIONS AND RPTED NO DAMAGE TO THE ARPT TXWY AREA. WE (THE FLC) OBSERVED NO DAMAGE TO THE ACFT.