RWY INCURSION AT CLE; OH; WHEN HOLD SHORT RWY BOUNDARY MARKINGS ARE MISINTERPED BY FLC.

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APPROX 15 SECONDS AFTER TOUCHDOWN; THE TWR CTLR INSTRUCTED US TO MAKE A 180 DEG TURN ON RWY 23R AND EXIT. UNABLE TO DO THIS; I CONTINUED DOWN TO INTXN K ON RWY 23R. APCHING INTXN K; THE CTLR ISSUED THE INSTRUCTION; 'HOLD SHORT OF RWY 23L ON TXWY K.' AS I APCHED THE INTXN; I OBSERVED THESE RWY/TXWY MARKINGS. BASED ON EXPERIENCE; I CROSSED OVER THE LINES (FIRST SET) AND THEN OBSERVED 'BROKEN' YELLOW LINES ON MY SIDE; SO I DECIDED TO CONTINUE AND THEN HOLD ON THE OTHER SIDE WHERE THE 'SOLID' DOUBLE YELLOW DICTATES PER THE AIM. IT WAS THEN THAT THE CREW REALIZED THAT WE WERE RAPIDLY APCHING RWY 23L. THE ACFT WAS STOPPED. NO INCIDENT/ACCIDENT OCCURRED. AFTER DISCUSSION WITH A TWR SUPVR; THE FOLLOWING CONCLUSIONS WERE DRAWN SO AS TO POSSIBLY AVOID THIS SCENARIO IN THE FUTURE: 1) PLTS SHOULD BE MORE AWARE OF NONSTANDARD TXWY MARKINGS THROUGH A REVIEW OF THE AIM. 2) CTLRS SHOULD NEVER ASSUME THAT ACR PLTS ARE FAMILIAR WITH AN ARPT THAT THEY ARE NOT BASED AT AND POSSIBLY CHANGE THE INSTRUCTION TO 'HOLD SHORT OF RWY 23L ON RWY 23.'