Nice rewrite. Although the connection between 
@ARGV = glob '/export/home/date_file*';

[download]
and 
while ( my $line = <> ) {

[download]
is not exactly obvious and could lead to some serious head-scratching. Especially if the program grows a bit further and actually uses command line arguments. Same as above, with explicit file open / close. 
#!/usr/bin/perl
use warnings;
use strict;

use List::Util qw(sum);

# Grab text files from archive directory with glob function
my @files = glob '/export/home/date_file*';

my %counts = (
    AB => 0,
    AC => 0,
    AD => 0,
    AE => 0,
    FG => 0,
);

for my $file (@files) {
    open my $fh, '<', $file
      or die "$file: $!";

    while ( my $line = <$fh> ) {
        my $var = substr $line, 41, 2;
        $counts{ $var }++ if exists $counts{ $var };
    }

    close $fh
      or die "$file: $!";
}

my $sum = sum values %counts;

for my $type ( keys %counts ) {
    print "$type\t: $counts{$type}\n";
}

print "Total     \t: $sum\n";

[download]

In reply to Re^2: Reading through a file and checking for a specific string by Monk::Thomas
in thread Reading through a file and checking for a specific string by vihar

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