#!/usr/bin/perl --

use strict;
use warnings;

use Tk;
use Data::Dump qw/ dd /;

my @tags = (
   "<KeyPress>",         "<KeyRelease>",
   "<ButtonPress>",      "<ButtonRelease>",
   "<FocusIn>",          "<FocusOut>",
   "<Expose>",           "<MapRequest>",
   "<ConfigureRequest>", "<ResizeRequest>",
   "<Activate>",         "<Deactivate>",
   "<Activate>",         "<Destroy>",
   "<Map>",              "<ButtonPress>",
   "<Button>",           "<Enter>",
   "<MapRequest>",       "<ButtonRelease>",
   "<Expose>",           "<Motion>",
   "<Circulate>",        "<FocusIn>",
   "<MouseWheel>",       "<FocusOut>",
   "<Property>",         "<Colormap>",
   "<Gravity>",          "<Reparent>",
   "<Configure>",        "<Key>",
   "<ResizeRequest>",    "<ConfigureRequest>",
   "<KeyRelease>",       "<Unmap>",
   "<Create>",           "<Leave>",
   "<Visibility>",       "<Deactivate>",
);
my $mw = tkinit();
$mw->Button(
    qw/ -text  exit -command /,
    sub {
        $Tk::widget->toplevel->destroy;
    }
)->pack;

my %seen;
for my $bindtag ( @tags ) {
    $mw->bind(
        $mw, $bindtag,
        sub {
            $seen{$bindtag}++;
            print qq{$bindtag \$e $Tk::event \$w $Tk::widget \@_ @_\n}
+;
        }
    );
}

my $redirect = 0;
$mw->geometry( '480x480+50+50' );
$mw->overrideredirect( $redirect = !$redirect );
$mw->withdraw;
$mw->deiconify;
$mw->raise;
$mw->repeat(
    1000,
    sub {
        $Tk::widget->overrideredirect( $redirect = !$redirect );
        $Tk::widget->deiconify;
        $Tk::widget->raise;
    }
);
dd \%seen;
$mw->MainLoop;
dd \%seen;
__END__
<Visibility> $e XEvent=SCALAR(0xf45c24) $w Tk::Button=HASH(0xf56344) @
+_ Tk::Button=HASH(0xf56344)
<Configure> $e XEvent=SCALAR(0xf648a4) $w MainWindow=HASH(0xf27a84) @_
+ MainWindow=HASH(0xf27a84)
<Expose> $e XEvent=SCALAR(0xf64864) $w MainWindow=HASH(0xf27a84) @_ Ma
+inWindow=HASH(0xf27a84)
<Key> $e XEvent=SCALAR(0xf28494) $w MainWindow=HASH(0xf27a84) @_ MainW
+indow=HASH(0xf27a84)
<FocusIn> $e XEvent=SCALAR(0xf647d4) $w Tk::Button=HASH(0xf56344) @_ T
+k::Button=HASH(0xf56344)
<KeyRelease> $e XEvent=SCALAR(0xf64794) $w Tk::Button=HASH(0xf56344) @
+_ Tk::Button=HASH(0xf56344)
<Destroy> $e XEvent=SCALAR(0xf56514) $w Tk::Button=HASH(0xf56344) @_ T
+k::Button=HASH(0xf56344)
<Destroy> $e XEvent=SCALAR(0xf27b84) $w MainWindow=HASH(0xf27a84) @_ M
+ainWindow=HASH(0xf27a84)
{
  "<Button>"        => 1,
  "<ButtonRelease>" => 1,
  "<Configure>"     => 36,
  "<Destroy>"       => 2,
  "<Enter>"         => 3,
  "<Expose>"        => 24,
  "<FocusIn>"       => 16,
  "<FocusOut>"      => 14,
  "<Key>"           => 96,
  "<KeyRelease>"    => 97,
  "<Leave>"         => 2,
  "<Map>"           => 25,
  "<Motion>"        => 21,
  "<Visibility>"    => 48,
}
[download]

Thank you. The answer it led me too, while counter intuitive, was FocusIn(A widget has gained the keyboard focus) is the 'only' event(at least in the provided tags) that is generated when a window in iconic state becomes visible. Your code helped me to find that!
Please note it had to be modified as the logic you employed does not see an Icon appear in Ubuntu Activities Bar so no user interaction viable to restore it once withdrawn.