You could try this:

use strict;
use warnings;
use POSIX;
use Perl::Unsafe::Signals;

my $appLog    = '/tmp/t.txt';
my $error     = 'Fatal Error';

exit            if (my $pid = fork);
defined($pid)   or die "Can't fork: $!";
POSIX:setsid()  or die "Can't setsid: $!";

my $tail      = open(LOG,"/usr/local/bin/tail -F $appLog|") 
        or die "Can't tail: $!";

$SIG{INT}     = sub {
   close LOG;
   kill 3, $tail;
   exit;
};
$SIG{TERM}    = $SIG{INT};
$SIG{PIPE}    = 'IGNORE';
$SIG{HUP}     = 'IGNORE';

UNSAFE_SIGNALS {
    while (<LOG>) {
       #&pageMe   if /$error/;
       print;
    }
};
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