RWY INCURSION AFTER AN S80 FLC IS DISTR WITH DUTIES AND CLRNC REGARDING RWY ASSIGNMENT DURING A NIGHT OP AT MMMX; FO.

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WITH AN FAA AIRWORTHINESS INSPECTOR IN THE JUMP SEAT; WE CROSSED A HOLD SHORT LINE ON TXWY B WHICH PLACED THE NOSE OF THE ACFT ACROSS AN EXTENDED RWY EDGE LINE FOR RWY 5L. WERE NOT HANDED OFF TO TWR; SO WE REQUESTED HDOF TO TWR. WHEN WE WERE INITIALLY CLRED TO TAXI; WE WERE TOLD TO FOLLOW AN ACFT AHEAD OF US. WE WERE CLRED TO RWY 5L; THE OTHER ACFT WAS CLRED TO RWY 5R. SINCE WE HAD EARLIER DISCUSSED THE POSSIBILITY OF USING RWY 5R; I GOT IN MY 'FOLLOW THE LEADER' MODE AND CONTINUED TO FOLLOW THE OTHER ACFT. AFTER WE HAD CROSSED THE HOLD SHORT LINE FOR RWY 5L; THE FAA INSPECTOR ASKED IF WE HAD BEEN CLRED TO CROSS RWY 5L AND WE IMMEDIATELY HELD OUR POS; TOLD TWR OF OUR WHEREABOUTS AND WERE CLRED TO CONTINUE OUR TAXI TO RWY 5R. FACTORS CONTRIBUTING TO OUR MISTAKE WERE: DARKNESS; POORLY LIT (IF LIT AT ALL); POOR PLACEMENT OF RWY SIGNS; FO HEADS DOWN IN COCKPIT; AND CAPT'S POOR SITUATIONAL AWARENESS. RWY 5L WAS NOT IN USE AT THE TIME. SUPPLEMENTAL INFO FROM ACN 562486: 2/3 OF THE WAY TO THE RWY; I (THE FO) SPILLED A CUP OF WATER ON MY APCH PLATES. MY ATTN WAS TAKEN AWAY FROM CRITICAL DUTIES OF CLRING AS I WAS CLEANING UP THE MESS. I ALSO ASKED THE CAPT IF HE WOULD LIKE RWY 5R FOR TKOF. HE REVIEWED THE ARPT DIAGRAM AND DECIDED NOT TO REQUEST RWY 5R. THE CAPT LATER CONFIDED THAT HE THOUGHT WE WERE CLRED TO FOLLOW THE ACFT. THAT ACFT WAS CLRED BY TWR TO TAXI TO RWY 5R.