MLG MISSES TAXIWAY; UNABLE CONTINUE. CLRED ONTO TAXIWAY NOT STRESSED FOR THEIR WT.

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WHILE TAXIING FOR DEP MISSED TURN ONTO PROPER TAXIWAY AND HAD NO WAY TO GET BACK TO SAME UNLESS TAXI ON TAXIWAY NOT RATED FOR WT OF MY ACFT. GND CTL DID ALLOW ME TO TAXI ON SURFACE RATED TO 65K; MY APPROX WT WAS 80K. BOTH FO AND MYSELF WERE BUSY WITH PRETKOF DUTIES. WE HAD BEEN CLRED TO AND JUST CROSSED AN ACTIVE RWY. WE WERE TO MAKE AN IMMEDIATE R TURN. INSTEAD; WE WENT STRAIGHT; ENTERING THE WRONG TAXIWAY WITH NOSE GEAR BEFORE STOPPING ACFT. LACK OF VIGILANCE WAS A CONTRIBUTING FACTOR IN THIS INCIDENT. CONTRIBUTING ALSO WAS FATIGUE -- WE HAD BEEN ON DUTY ALMOST 8 HRS IN WHAT WAS A 13 (12:47) HR DAY WITH 7 TKOFS AND LNDGS. I THINK ALSO THE TAXIWAY SIGNAGE MAY ALSO BE POORLY VISIBLE WHILE XING RWY. CANNOT SEE IT PLAINLY UNTIL INTO INTXN WHERE TURN IS TO BE MADE. SUPPLEMENTAL INFO FROM ACN 209546: LACK OF VIGILANCE WAS A CONTRIBUTING FACTOR. FURTHER; FATIGUE PLAYED A CONTRIBUTION AS WE WERE IN HR 8 OR 13 HR DAY. LASTLY; THE TAXIWAY SIGNS WERE NOT AS CLRLY MARKED AS THEY SHOULD HAVE BEEN.