Hmmm...Maybe Show needs to be handled differently. I tried this, but I used a different geometry. 
#!/usr/bin/perl 

use strict;
use warnings;
use Tk;
use Tk::widgets qw/DialogBox/;
require Tk::LabEntry;

my $uname = 'Anonymous';
my $pw    = 'Anonymous';
my $mw    = MainWindow->new(
    -screen => $ARGV[0] || $ENV{'DISPLAY'},
    -bg => 'black',
);
$mw->withdraw;

my $box = $mw->title('Test');
$box = $mw->geometry('-1+1');
$box = $mw->DialogBox(
    -title          => 'Login',
    -buttons        => [ 'OK', 'Quit' ],
    -fg             => 'red',
    -default_button => 'OK',
);
$box->add(
    'LabEntry',
    -textvariable => \$uname,
    -width        => 20,
    -bg           => 'black',
    -fg           => 'green',
    -label        => 'Username',
    -labelPack    => [ -side => 'left' ]
)->pack;
$box->add(
    'LabEntry',
    -textvariable => \$pw,
    -bg           => 'black',
    -fg           => 'green',
    -width        => 20,
    -label        => 'Password',
    -show         => '*',
    -labelPack    => [ -side => 'left' ]
)->pack;
$box->Show( -popover => $mw );

MainLoop;

[download]
Updated; Added $mw->withdraw

In reply to Re^3: Tk multiple monitor problem by Khen1950fx
in thread Tk multiple monitor problem by JohnRS

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