UNAUTHORIZED RWY XING BY CORP JET.

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CLRED TO TAXI TO RWY 13 FOR TKOF. PARKING IS ON NE SIDE OF RWY. NORMAL PROC IS TO CROSS RWY 13; THEN TAXI ON SW SIDE TO APCH END OF RWY. GND CTL CLRED US TO TAXI TO RWY 13. PLT NOT FLYING CALLED FOR TAXI CLRNC BUT DIDN'T HAVE EAR PIECE ON; SO DIDN'T HEAR TAXI CLRNC. I ANTICIPATED XING RWY 13 AND HAD THAT MINDSET. GND CTL DID NOT INSTRUCT US TO HOLD SHORT OF RWY 13 INTXN. AS I CROSSED RWY; PNF ASSUMED WE'D BEEN CLRED ACROSS (AGAIN; HE/WE DIDN'T HEAR INITIAL TAXI CLRNC.) I OPERATED INTO THIS ARPT FOR SEVERAL YRS; PRIOR TO THE RECENT ESTABLISHMENT OF A CTL TWR AND APPARENTLY STILL HAVE A MINDSET OF AN UNCTLED ARPT. CORRECTIVE ACTIONS. I NEED TO BE MORE ATTENTIVE. AS DISCUSSED IN POST FLT DEBRIEFING; PNF NEEDS TO BE MADE VOCAL WHEN HE HAS DOUBTS OR CONCERNS. HE ADMITTED HE WAS CONCERNED ABOUT OUR RWY XING; BUT ASSUMED THAT WE HAD BEEN CLRED. GND CTLR COULD HAVE BEEN MORE SPECIFIC IN HIS TAXI INSTRUCTIONS. EITHER CLR US TO TAXI ON THE NE TAXIWAY (PRECEDING THE NEED TO CROSS THE RWY) OR CLR US TO TAXI VIA THE SW TAXIWAY AND HOLD SHORT OF THE RWY. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR EXPLAINED THAT TXWY ON SW SIDE OF RWY HAS MORE WING TIP CLRNC AS ACFT ARE PARKED NEAR THE TXWY ON NE SIDE OF RWY. THEY PARK ON NE SIDE BUT TWR USUALLY GIVES TAXI ACROSS TO SW SIDE FOR RWY 13 DEP. IT IS ALSO NORMAL OP FOR ACFT TO LAND ON 31 AND TKOF OPPOSITE DIRECTION ON 13. THIS IS DUE TO HIGH TERRAIN AND NOISE ABATEMENT NW OF ARPT. THERE WERE NO OTHER ACFT OR VEHICLES INVOLVED.