MLG ACFT DURING TAXI FAILED TO MAKE THE PROPER TURN ONTO TXWY AND CROSSED A RWY. NIGHT; WX AND FATIGUE WERE FACTORS.

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THIS INCIDENT OCCURRED ON FIRST FLT ON SECOND DAY OF A 3 DAY TRIP AT XB00 AM WITH A RPT TIME OF XA00 AM. FLT WAS SCHEDULED TO DEPART AUSTIN AT XB00 AM. THE CAPT AND MYSELF REVIEWED A 10-7 ARPT DIAGRAM PAGE FOR PROBABLE TAXI RTE. AFTER PUSHBACK AND ENG START; I CALLED FOR A TAXI CLRNC. WE WERE INSTRUCTED TO TAXI VIA TXWY H AND TXWY L AND HOLD SHORT OF RWY 17; WHICH I REPEATED BACK. WE TAXIED ACROSS THE RAMP TO TXWY L AND WERE ESTABLISHED ON THE TXWY WHEN THE CAPT CALLED FOR THE TKOF CHKLIST. I WAS INVOLVED WITH THE BEFORE TKOF CHK; BUT KEPT THE LIGHT DIM SO I COULD KEEP A PARTIAL WATCH OUTSIDE TO HELP MONITOR OUR TAXI. WE SUDDENLY NOTICED WE WERE COMING UP ON RWY 13L AFTER XING RWY 13R WHEN WE BOTH REALIZED WE HAD MISSED THE TURN FOR THE TXWY H; AND HAD NOT SEEN A SIGN FOR IT. WE CONTACTED TWR WHO ADVISED US THAT THE PORTION OF THE TXWY WE WERE NOW ON WOULD NOT SUPPORT OUR ACFT. (THERE IS NO MENTION OF THIS ON THE 10-7 PAGE AND WE WERE STILL ON TXWY L.) WE THEN ASKED IF WE COULD TURN R (S) ON RWY 13L; BACK TO TXWY P TO REJOIN TXWY L AND TXWY H; WHICH TWR CTL AUTH. RWY 13R WAS THE ORIGINAL ACTIVE RWY WE WERE TAXIING TO. WE CONTINUED THE TAXI BACK TO RWY 13R; AND CONTINUED THE FLT WITHOUT INCIDENT. CONTRIBUTING FACTORS: IT WAS DARK AND MARGINAL IFR (HALF MI; DRIZZLE AND MIST) AND THE TWR COULD NOT MONITOR OUR PROGRESS. WE WERE NOT FAMILIAR WITH THE ARPT. WE HAD EXPECTED A DIFFERENT TAXI RTE WHICH WOULD STILL HAVE US HOLDING SHORT OF RWY 17; BUT XING ACTIVE RWY 13R FIRST. COCKPIT LIGHTING WAS DIM TO HELP US SEE OUT IN MARGINAL VISIBILITY AND WAS DISTR WITH RUNNING A CHKLIST. WE BOTH THOUGHT TXWY H WAS WHERE TXWY F WAS; WHICH WOULD HAVE TAKEN US THE RTE WE THOUGHT WE WOULD GET ORIGINALLY. THE CAPT WAS ALSO USED TO HOUSTON HOBBY; WHICH HAS A SIMILAR LAYOUT. ON THE SECOND TIME AROUND WE SAW TXWY H. ALL OTHER SIGNS HAD BEEN ON BOTH THE R AND L; WHEREAS TXWY H SIGN WAS ONLY ON THE L; SO I COMPLETELY MISSED IT THE FIRST TIME SITTING ON THE R SIDE OF THE ACFT. ALSO; THE SIGN WAS VERY DIMLY LIT; SET BACK FROM THE TXWY AND NOT RIGHT AT THE INTXN WHERE WE WOULD EXPECT TO SEE IT. IN ADDITION; NEITHER OF US SLEPT WELL THAT NIGHT DUE TO EXCESSIVE NOISE AT THE HOTEL AND A VERY NOISY AIR CONDITIONER; AND A WAKE UP TIME OF XX00 AM IN ORDER TO BE AT THE ARPT BY YY00 AM. ALTHOUGH WE DIDN'T FEEL FATIGUED AT THE TIME; I AM SURE THE LACK OF SLEEP CONTRIBUTED. FORTUNATELY; OUR VIGILANCE FOR ALWAYS CHKING ACTIVE RWYS BEFORE XING HELPED INSURE WE DIDN'T TAXI ACROSS RWY 13R WHEN AN ACFT WAS TAKING OFF OR LNDG. TO PREVENT FUTURE PROBS OF THIS TYPE; THE TXWY SIGN FOR TXWY H SHOULD BE MOVED CLOSER TO THE INTXN AND MADE BRIGHTER; POSSIBLY LARGER; ALONG WITH A SIGN INDICATING WE ARE APCHING THIS TXWY. IT WOULD HELP TO PUT A SIGN ON THE R SIDE (OPPOSITE THE TXWY) ALSO; SO THE FO CAN HELP MONITOR TAXI PROGRESS WHILE INVOLVED IN OTHER DUTIES. AND; OF COURSE; ENSURING FLCS HAVE QUIET PLACES FOR REST TO GET PROPER SLEEP WITHOUT INTERRUPTIONS; ESPECIALLY WHEN VERY EARLY WAKE- UPS. ADDENDUM: I HAVE SINCE TALKED TO 2 OTHER PLTS WHO HAVE MADE THE SAME EXACT MISTAKE AT AUSTIN (AND THEY DID FILE NASA REPORTS ALSO). THERE IS DEFINITELY A PROB AT THIS ARPT.