In addition to what the other replies above have said (which is the way I would do it), I would strongly recommend using @ARGV to get your input parameters (input file name and pattern to look for). Something like this:

#!/usr/local/bin/perl

use strict;
use warnings;

my $Usage = "Usage:  $0  search-pattern  data.file\n";
( @ARGV == 2 and -f $ARGV[1] ) or die $Usage;

my ( $pattern, $ifile ) = @ARGV;
open( IN, "<", $ifile ) or die "$ifile: $!\n$Usage";
$/ = "\n1";  # use FORTRAN page break as input record separator

my $opattern = $pattern;
$opattern =~ s/[^\w.-]/_/g;      # limit range of characters to be
my $ofile = "$ifile.$opattern";  # used in output file name
open( OUT, ">", $ofile ) or die "$ofile: $!\n";

while (<IN>) {
    print OUT if ( /\n0 EID:\s+$pattern\s+/ );
}
close OUT;
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When you do it that way, it's easier to automate multiple runs (extract a given pattern from several files, or several patterns from one file, or several patterns from several files, etc...), as well as being easier, quicker and less error-prone to run the script manually.