H25B CREW HAD A TXWY AND RWY INCURSION AT CLE.

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FLC ARRIVED AT RAMP OF CLE FBO 15 MINS AFTER SUNSET FOR REFUEL QUICK TURN. WHEN READY TO TAXI; IT WAS ABOUT 45 MINS AFTER SUNSET BUT RAMP WAS FLOODED WITH LIGHT FROM POLES. BEFORE MOVING OUT OF PARKING; PNF HAD TO CALL GND TWICE FOR TAXI CLRNC. BOTH PLTS WERE USING HEADSETS. WHEN GND CTL GAVE CLRNC; IT WAS READ BACK BUT NOT WRITTEN DOWN AS '...TAXI TO RWY 24C VIA TXWY L2; TXWY L; HOLD SHORT OF TXWY W.' THERE WAS NO CORRECTION OR RESPONSE FROM GND. PF BEGAN TAXI WHILE PNF ASSURED PF OF GOOD RAMP OBSTACLE CLRNC OFF THE R SIDE. WHEN CLR OF RAMP; PNF HAD ATTN INSIDE FOR TAXI CHKLIST. GND CALLED WHILE ACFT WAS ON TXWY L; PAST TXWY H; TO SAY HE HAD CLRED US TO HOLD SHORT OF TXWY K; 2 TXWYS BEHIND. PNF LOOKED UP AND OUTSIDE TO SEE AN ACFT ROLLING OUT ON RWY 24L; PARALLEL TO TXWY L. PF STATED TO PNF THAT WE WERE CLRED TO HOLD SHORT OF TXWY T; SO PNF RELAYED THAT TO GND. WITHOUT FURTHER COMMENT; GND GAVE CLRNC TO TAXI 'TXWY L; TXWY V; HOLD SHORT OF TXWY W.' THE PNF'S READBACK AGAIN WENT UNCONFIRMED BY GND AND REST OF TAXI WAS UNEVENTFUL. THE CONTRIBUTING FACTORS AND FLC CORRECTIVE ACTIONS FOR THE FUTURE ARE: 1) PNF NOT WRITING DOWN TAXI CLRNC. 2) GND CTL NOT CONFIRMING READBACKS. 3) GND CTL NOT STATING REASON FOR HOLDING SHORT. DOING SO WOULD INCREASE PLT SITUATIONAL AWARENESS; CREATING EXTRA 'BUY-IN' FROM FLC MEMBERS. 4) FLC SHOULD SLOW DOWN TAXI CHKLIST TO MINIMIZE DISTR WHEN HOLDING SHORT AT UNFAMILIAR; BUSY ARPTS AT NIGHT. 5) FLC SHOULD CONFIRM WITH EACH OTHER ANY HOLD SHORT POINT; DOUBLECHK TAXI CHART; AND IF A QUESTION EXISTS; GET IT CLARIFIED WITH ATC. 6) CURRENT ATIS AT CLE REMINDS PLTS TO READ BACK RWY ASSIGNMENTS AND HOLD SHORTS; INDICATING THAT CLE HAS A PROB WITH TAXI MISCUES. SUPPLEMENTAL INFO FROM ACN 566108: THE GND CTLR WAS TALKING VERY FAST WITH LITTLE TIME TO REPLY. WE FEEL IF HOLD SHORT OPS ARE TO BE USED THEN THE CTLRS NEED TO SLOW DOWN AND BE MORE SPECIFIC. THIS IS ONLY THE SECOND TIME IN MY 20+ YR CAREER I HAVE FLOWN INTO CLE.