What you probably want is to separate the reads into different files. Here is a quick script I whipped up with some code duplication but all in the name of being a little more efficient.

Run it as:

python split.py data.fq 1 > pair1.fq

or

python split.py data.fq 2 > pair2.fq

to split the pairs into different files.

import sys

fname, mode = sys.argv[1:]

def parse(stream):
    for id in stream:
        id = id.strip()
        seq = stream.next().strip()
        tmp = stream.next().strip()
        qual = stream.next().strip()
        yield id, seq, tmp, qual

stream = file(fname)

if mode == "1":

    for id, seq, tmp, qual in parse(stream):

        half = len(seq)/2
        seq  = seq[:half]
        qual = qual[:half]

        print id
        print seq
        print tmp
        print qual

else:

    for id, seq, tmp, qual in parse(stream):

        half = len(seq)/2
        seq  = seq[-half:]
        qual = qual[-half:]

        id = id[:-1] + "2"
        tmp = tmp[:-1] + "2"

        print id
        print seq
        print tmp
        print qual

Awk (long) one liner:

zcat GM12878/wgEncodeCshlLongRnaSeqGm12878CellTotalFastqRep1.fastq.gz | awk '{OFS="\n"; \
print $0 >"pair.R1.fq"; \ 
sub("#0/1$","#0/2",$0); \ 
print $0 >"pair.R2.fq";  \
getline seqs; \
seqs1 =substr(seqs,0,length(seqs)/2); \
seqs2 =substr(seqs,1+length(seqs)/2,length(seqs)/2); \
getline; \
getline quals; quals1 =substr(quals,0,length(quals)/2);  \
quals2 =substr(quals,1+length(quals)/2,length(quals)/2); \
print seqs1, "+", quals1 >>"pair.R1.fq" ; print seqs2, "+", quals2 >> "pair.R2.fq"  }'

Perl option:

*edited to write output in separated files, not stdout/stderr

#!/usr/bin/perl

use strict;
use warnings;

my $file1 = shift @ARGV;
my $file2 = shift @ARGV;
open O1, ">$file1" or die;
open O2, ">$file2" or die;
my $n = 0;
while (<>) {
    $n++; 
    chomp; 
    if ($n % 2 == 0) { 
        print O1 substr($_, 0, int((length $_) / 2)), "\n"; 
        print O2 substr($_, int((length $_) / 2) + 1), "\n"; 
    }
    else { 
        print O1 "$_\n"; 
        s/1$/2/; 
        print O2 "$_\n"; 
    }
}
close O1; 
close O2;

Execute in bash as:

zcat GM12878/wgEncodeCshlLongRnaSeqGm12878CellTotalFastqRep1.fastq.gz | perl splitFastq.pl reads_1.fq reads_2.fq