LGT TAXIED FROM TAXIWAY ONTO A VEHICLE ROAD AND BECAME STRANDED.

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WHILE TAXIING OUT ON THE INNER TAXIWAY TO 36R WE CONTINUED PAST THE END OF THE TAXIWAY ONTO A SMALL TAXIWAY EXTENSION; CLOSED TO LARGE ACFT. THERE WAS LIGHT RAIN AT THE TIME; THE WINDSHIELD WIPERS WERE NOT ON AND THE TAXIWAY WAS 'SHINY' WET HELPING OBSCURE THE TAXIWAY MARKINGS. ALTHOUGH NOT SHOWED ON THE ARPT DIAGRAM (60-9) THERE IS A HARD SURFACE EXTENSION TO THE RWY AND AN ACCESS ROAD AT THE END OF THE TAXIWAY GIVING AN ILLUSION THAT IT IS NECESSARY TO CONTINUE ON THE SMALLER TAXIWAY TO REACH THE END. (SEE ATTACHED DIAGRAM). ADDING TO THE CONFUSION; WE WERE CLRED FOR TKOF AS WE APCHED THE END OF THE INNER. I WAS SETTING MY HDG BUG AND MAKING A LAST MIN SCAN INSIDE THE COCKPIT. THE COPLT WAS CONFUSED BECAUSE TKOF CLRNC CAME ON GND FREQ WHILE STILL ON THE INNER. THE SO WAS DOING HIS LAST MIN ITEMS. WE ALL REALIZED AT THE LAST SECOND WHAT WAS HAPPENING. ALTHOUGH I COULD HAVE 'SLAMMED' ON THE BRAKES AND MAYBE STOPPED JUST BEFORE ENTERING THE EXTENSION; I FELT A PANIC STOP WOULD NOT BE GOOD FOR THE ACFT AND/OR PAX AND SINCE SAFETY WAS NOT COMPROMISED; I ELECTED TO BRING THE ACFT TO A SMOOTH STOP. WE THEN NEEDED A TUG TO PUSH US BACKWARD TO THE MAIN TAXIWAY. WE THEN CONTINUED TO ORD. WE WERE TOLD BY THE TUG DRIVER THAT THIS WAS NOT THE FIRST TIME HE HAD TO DO THIS AND IT PROBABLY WON'T BE THE LAST. BY THE TIME WE WERE PUSHED BACK THE SUN WAS OUT AND THE TAXIWAYS WERE DRY. ALL 3 OF US WERE SURPRISED TO SEE THE LARGE YELLOW X; SMALL RED WARNING SIGN AND 4 RED END LIGHTS (NOT ON). SOMETHING ELSE I FORGOT TO ADD: THE YELLOW CTRLINE CONTINUES FROM THE TAXIWAY ONTO THE EXTENSION FURTHER ADDING TO THE ILLUSION THAT IT IS NECESSARY TO CONTINUE FURTHER ON THE TAXIWAY TO REACH THE END OF RWY 36R. I MADE A SUGGESTION TO THE COMPANY THAT A COMMENT ABOUT THIS POSSIBLE ILLUSION BE MADE ON OUR 60-7 PAGE.