FLC OF A B757 STARTED TKOF WHEN THE 'RUDDER RATIO' LIGHT WAS LIT BUT WENT OUT WHEN TKOF PWR WAS APPLIED.

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WHEN WE ARRIVED AT THE STATION WE HAD A RUDDER RATIO LIGHT ILLUMINATED. WE WROTE IT UP AND MAINT CLRED THE WRITE UP BY RESETTING CIRCUIT BREAKERS. UPON TAXIING OUT OF THE STATION THE LIGHT ILLUMINATED AGAIN. THE FO AND I TALKED IT OVER AND DECIDED IT WOULD BE OK TO TKOF WITH THE PROB. THE LIGHT WENT OUT WHEN THE PWR CAME UP FOR TKOF. HOWEVER; IF IT HAD NOT; A POSSIBLE ENG OUT CTL PROB COULD HAVE HAPPENED WHICH NEITHER OF US THOUGHT OF AT THE TIME. CONTRIBUTING FACTORS WERE FATIGUE (LONG DUTY DAY); POOR INTERACTION BTWN CAPT AND FO AND A LITTLE GET HOMEITIS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THAT THE ACFT WAS A B757 AND THE INCIDENT LOCATION WAS WASHINGTON NATIONAL ARPT; DC. HE MAINLY SUBMITTED THE RPT TO PROVIDE THE HUMAN FACTORS WITH REGARD TO THE FATIGUED ATTITUDE OF THE FLC IN GOING AHEAD WITH THE TKOF EVEN THOUGH THE WARNING LIGHT REAPPEARED DURING THE INITIAL START OF TKOF. HOWEVER; FORTUNATELY; THE LIGHT WENT OUT WHEN PWR WAS ADJUSTED FOR TKOF.