G'day elef,

From your description, it sounds like Tk::Optionmenu is what you're after. If you look in the widget demo, you'll see examples under "Menus: 3. Menubuttons.": there's sample code for Optionmenu() as well as a native_optionmenu() subroutine — one of these should be suitable.

However, if you really must use Tk::BrowseEntry, this seems to do what you want:

#!/usr/bin/env perl

use strict;
use warnings;

use Tk;
use Tk::BrowseEntry;

my $mw = MainWindow->new;
$mw->geometry('300x400+50+50');

my $ctrl_F = $mw->Frame->pack(-side => 'bottom');
$ctrl_F->Button(-text => 'Exit', -command => sub { exit })->pack;

my $app_F = $mw->Frame->pack(-side => 'top', -fill => 'both', -expand 
+=> 1);
my $be_var;
my $be = $app_F->BrowseEntry(-variable => \$be_var);
$be->insert(end => "Option $_") for 1 .. 9;
$be->pack;

$be->Subwidget('entry')->packForget;

MainLoop;
[download]

The entry box never appears.

The listbox doesn't shift to the left (which you mentioned in another part of this thread). The default -side for pack() is 'left': perhaps look at whatever you've used for this.

I wasn't entirely sure what you meant by "I just want the arrow button to be visible until it's clicked.". I'm on a *nix system: when the listbox appears, it covers the button. When I specified -style => 'MSWin32', the listbox appeared just below the button; with -style => 'unix', it returned to my OS's default of covering the button: perhaps consider that setting to get the look-and-feel you're after.