Here's how I'd do it.

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11117902
use warnings;
use Tk;
use Tk::IO;

my $date = localtime();

my $mw = MainWindow->new;
$mw->Button(-text => 'Start', -command => \&start,
  )->pack(-side => 'top', -fill => 'x');
$mw->Label(-textvariable => \$date, -fg => 'blue',
  )->pack(-side => 'top', -fill => 'x');
$mw->Button(-text => 'Exit', -command => sub {$mw->destroy},
  )->pack(-side => 'bottom', -fill => 'x');
$_ = $mw->Text(-width => 10, -font => 14,
  )->pack(-side => 'left') for my( $one, $two );

$mw->repeat( 1000, sub { $date = localtime() } );

MainLoop;

sub start
  {
  Tk::IO->new(-linecommand => sub {
    $one->insert(end => shift);
    $one->see('end');},
    )->exec('for i in `seq 1 24` ; do sleep .5 ; echo $i ; done');

  Tk::IO->new(-linecommand => sub {
    $two->insert(end => shift);
    $two->see('end');},
    )->exec('for i in `seq 1 24` ; do sleep .7 ; echo $i ; done');
  }
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Note that the date keeps advancing while the text widgets are being filled in, indicating that the gui is still responding.