I would expect the relay to switch on at the same time as "ON" is printed - in other words 1s later than it does. Doing a bit of experimenting shows that it actually switches on not at print $value "0"; but when the direction is set to out at close $direction;.

The files in /sys/ are actually kernel drivers, much like in /proc/. Those file-based drivers are rather simple-minded and desigend to use by shell scripts, where each echo foo > /proc/some/magic/file ends in calling open(2), write(2), and close(2). So you should simulate that behaviour.

At work, I had a client project where a Raspi was involved, running a daemon for a different purpose. Some more I/Os were needed, and so I added a tiny C module that implemented functions to configure and functions to set pins. Both just simulated a shell echo, i.e. called open, write, close. I/O switching was fast enough not to see a delay with the naked eye, so probably below 100 msec.

Rewriting your code like this should help:

#!/usr/bin/perl 

# untested!

use strict;
use warnings;
use feature "say";

sub write_file
{
    my ($fn,$content)=@_;
    open my $f,'>',$fn or die "Could not open $fn: $!";
    say $f $content;
    close $f;
}

sub export
{
    my $number=shift;
    write_file("/sys/class/gpio/export",$number);
}

sub direction
{
    my ($number,$dir)=@_;
    write_file("/sys/class/gpio/gpio$number/direction",$dir);
}

sub write_value
{
    my ($number,$level)=@_;
    write_file("/sys/class/gpio/gpio$number/value",$level);
}

sub read_file # unused
{
    open my $f,'<',$fn or die "Could not open $fn: $!";
    my $line=<$f>;
    close $f;
    chomp $line;
    return $line;
}

sub read_value # unused
{
    my $number=shift;
    return read_file("/sys/class/gpio/gpio$number/value");
}

# all of the functions above could move to a module 

export(20);
direction(20,"out");

while (1) {
    write_value(20,0);
    say "on";
    sleep 1;
    write_value(20,1);
    say "off";
    sleep 1;
}
[download]

Alexander