B737 FLC ALMOST HAVE A RWY INCURSION AFTER THEY BECOME CONFUSED REGARDING THE TWR INSTRUCTING THEM TO FOLLOW ANOTHER B737 AFTER LNDG.

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FLT FROM LAS TO EWR LANDED AT NEWARK ON RWY 04R AND TAXIED CLR OF RWY AT TXWY K INTERSECTION. EWR TWR INSTRUCTED US TO FOLLOW A PRECEDING B737 ON KILO AND TAXI S ON PAPA AND TO REMAIN WITH HIM. THE B737 WE WERE FOLLOWING CONTINUED AHEAD ON KILO AND CROSSED RWY 04L. AS WE JOINED TXWY KILO FOLLOWING THE B737; WE COMPLETED THE AFTER LNDG CHKS AND LOOKED AT THE TXWY DIAGRAM FOR PAPA TXWY AND MISS THE PAPA TXWY SIGN. WE CONTINUED AHEAD ON KILO TXWY AND WE APCHED THE PARALLEL RWY 04L; I SIGHTED AN ACFT ON THE RWY AND THE CAPT STOPPED THE ACFT AT THE RWY HOLD SHORT LINE. AS WE STOPPED THE ACFT; THE TWR INSTRUCTED US TO HOLD OUR POS. WHILE HOLDING SHORT; WE THEN DETERMINED THAT TXWY PAPA WAS BEHIND US. TWR CLRED US ACROSS RWY 04L AND SWITCHED US TO GND CONTROL. WE TAXIED TO THE GATE UNEVENTFULLY. INSTRUCTIONS TO FOLLOW THE B737 TFC; WHICH WAS TAXIING IN ON A DIFFERENT RTE WAS DISTRACTING. EASIER TAXI INSTRUCTIONS WOULD HAVE BEEN TO MAKE FIRST L TURN ON TXWY PAPA; RATHER THAN 'TAXI S ON PAPA;' WHICH PUTS EYES FROM OUTSIDE TO THE CHART TO LOOK FOR TXWY PAPA.