RWY INCURSION BY A B737-800 FLC WITH ANOTHER ACR ABOUT TO ROLL ON RWY 34R AT SEATAC; WA.

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FLT ACR X LANDED ON RWY 34L SEATTLE. DURING LNDG ROLLOUT; TWR INSTRUCTED; 'ACR X TURN R AND R AGAIN; HOLD SHORT RWY 34R.' I READ BACK; 'ACR X; 2 R TURNS; HOLD SHORT RWY 34R.' AFTER CLRING RWY 34L AT TXWY H; I STARTED MY AFTER LNDG CHKLIST FLOW. THE CAPT ASKED; 'ARE WE CLRED ACROSS RWY 34R?' I SAID; 'NO' AND HE IMMEDIATELY STOPPED THE ACFT. I CALLED THE TWR AND SAID 'STOP ACR Y'S TKOF ON RWY 34R; OUR NOSE IS 3 FT OVER THE LINE.' ACR Y STOPPED HIS TKOF AND TAXIED CLR AT TXWY N OR TXWY M. WE WERE CLRED ACROSS RWY 34R AND LATER TOLD TO PHONE THE TWR. CONTRIBUTING FACTORS: 1) FATIGUE: IT WAS XA00 BODY TIME AND WE HAD FLOWN 7 HRS OF FLT TIME THAT DAY. 2) LOW TIME: I HAD 40 HRS IN MODEL; THE CAPT 120 HRS. 3) DARKNESS: THE AREA BTWN RWY 34L&R IS A DARK AREA. 4) DISTR: I BEING NEW TO THE ACFT; SO I WAS DOUBLECHKING MYSELF TO ENSURE COMPLETION OF THE AFTER LNDG CHKLIST. 5) UNUSUAL TAXI INSTRUCTIONS: THE 2 R TURNS; A HIGH SPD TO A REVERSE HIGH SPD GAVE A STRANGE ANGLE TO THE RWY LIGHTS OF RWY 34R.