Here's two ways you can stop the button from being repeatedly invoked:

1. Check if the Toplevel already exists.
2. Use a local grab.

Checking for existence:

use strict;
use warnings;

use Tk;

my $mw = MainWindow->new();

my $single_tl;

$mw->Button(-text => 'Open Toplevel',
    -command => sub {
        if (Exists($single_tl)) {
            $mw->messageBox(-message => 'Already Open');
        }
        else {
            $single_tl = $mw->Toplevel();
            $single_tl->Button(-text => 'Close',
                -command => sub { $single_tl->destroy(); },
            )->pack();
        }
    },
)->pack();

$mw->Button(-text => 'Exit', -command => sub { exit })->pack();

MainLoop;
[download]

Using a grab:

use strict;
use warnings;

use Tk;

my $mw = MainWindow->new();

$mw->Button(-text => 'Open Toplevel',
    -command => sub {
        my $single_tl = $mw->Toplevel();
        $single_tl->Button(-text => 'Close',
            -command => sub { $single_tl->destroy(); },
        )->pack();
        $single_tl->grab();
    },
)->pack();

$mw->Button(-text => 'Exit', -command => sub { exit })->pack();

MainLoop;
[download]

Please note that both of these pieces of code are self-contained, will run without requiring further code and are not cluttered with irrelevant, cosmetic instructions (e.g. changing colours, resizing windows and so on). Please read How do I post a question effectively? paying particular attention to "... a minimal script that reproduces your problem ..."

Furthermore, your zig-zag indentation is not particularly easy to ready. Please choose an indentation style and use it. perlstyle may help you with this.

You've received help on quite a few questions you've posted in recent weeks. Consider helping those who are helping you.