AFTER LNDG AND RECEIVING TAXI INSTRUCTIONS; B737 PIC MISSES PARALLEL RWY HOLD SHORT LINE. AFTER ADVISING DEP TFC OF B737 POS; DEP CLRED FOR TKOF WITHOUT FURTHER DISCUSSION.

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AFTER LNDG ON RWY 4R AT EWR; TWR CTLR CLRED ACFT TO EXIT L OFF AND HOLD SHORT OF RWY 4L AND TO REMAIN ON TWR FREQ. DISTANCE BTWN RWYS 4R AND 4L IS SHORT WITH TXWY P IN BTWN. AFTER EXITING RWY; I STARTED AFTER LNDG PROCS; NOT CHKLIST; AS ACFT WAS SLOWING. I LOOKED OUTSIDE JUST AS CAPT ASKED IF WE WERE CLRED TO CROSS; OR HOLD SHORT. AS HE WAS ASKING THE QUESTION; I SAID HOLD SHORT; HOLD SHORT. AT THAT TIME THE CAPT STOPPED THE ACFT IMMEDIATELY; APPROX 8-10 FT PAST THE HOLD SHORT LINE; BUT WELL CLR OF THE RWY; BY APPROX 20-30 FT. IT WAS AT THIS TIME WE NOTICED LIGHTS COME ON ON AN ACFT STARTING ITS DEP ROLL. ACFT LIFTED OFF APPROX MID-FIELD; SOME 2500 FT PRIOR TO OUR POS. NO EVASIVE ACTION WAS TAKEN BY EITHER ACFT. TWR CTLR SAID SOMETHING TO THE DEPARTING ACFT ABOUT CAUTION ACFT IN SAFETY ZONE(?); BUT DID NOT TELL THEM TO ABORT. AGAIN; NO EVASIVE ACTION WAS TAKEN BY EITHER ACFT. I DON'T RECALL WHETHER OR NOT WE WERE CLRED TO CROSS TXWY P AND HOLD SHORT RWY 4L OR JUST HOLD SHORT RWY 4L. POSSIBLY THIS IS WHERE THE CAPT GOT CONFUSED. JUST A CLRNC TO HOLD SHORT OF RWY 4L WITHOUT ANY CLRED TO CROSS INSTRUCTIONS WOULD CERTAINLY AVOID ANY CONFUSION. MAYBE A MANDATORY STOP PRIOR TO RWY 4L; ETC; WOULD BE IN ORDER. OBVIOUSLY; A LITTLE MORE CAUTION AND DILIGENCE OR CONCERN WOULD BE IN ORDER. SUPPLEMENTAL INFO FROM ACN 427454: OUR HOLD SHORT CLRNC; WHILE QUITE ROUTINE FOR THE CTLR I'M SURE; IS GIVEN AT A BUSY TIME IN THE COCKPIT AND POSSIBLY FULL ATTN MAY NOT BE ALWAYS POSSIBLE. I'M NOT SURE IF THERE IS A FIX EXCEPT EXERCISING MORE CAUTION.