It looks like you're using Test::Class. That module is specifically designed to handle situations like this. In particular, every method is called with an invocant which in this case is a blessed, empty hashref. You're allowed (even encouraged!) to shove things in that hashref. For test classes, I like to call my invocant $test instead of the standard $self.

sub Start_timer : Test(startup) {
  my $test = shift;
  my $start = time();
  cprint "#\x037Started at ", (strftime '%A %d %B %Y %H:%M:%S',localti
+me($start)), "\x030\n";
  $test->{start} = $start;
}

sub End_timer : Test(shutdown) {
  my $test = shift;
  my $start = $test->{start};
  my $end = time;

  cprint "#\x037Ended at ", (strftime '%A %d %B %Y %H:%M:%S', localtim
+e($end)),"\x030\n";

  cprintf "#\x035 Total run time=>", $end-$start, " seconds\n";
  cprintf ("%02d:%02d:%02d\x030\n",(gmtime($end-$start))[2,1,0]);
}
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However, this is a practice I discourage. First, it's easy to write something like $test->{strat}; and wonder why you didn't get a value. Second, encouraging people to reach inside of objects like that is generally a bad idea.

Another solution would be to look at Test::Class::Moose and use proper attributes.

has 'start' => (
  is      => 'ro',
  isa     => 'Int',
  default => sub { return time },
);

sub test_startup {
  my $test = shift;
  my $start = $test->start;
  cprint "#\x037Started at ", (strftime '%A %d %B %Y %H:%M:%S',localti
+me($start)), "\x030\n";
}

sub test_shutdown {
  my $test = shift;
  my $start = $test->start;
  my $end = time;

  cprint "#\x037Ended at ", (strftime '%A %d %B %Y %H:%M:%S', localtim
+e($end)),"\x030\n";

  cprintf "#\x035 Total run time=>", $end-$start, " seconds\n";
  cprintf ("%02d:%02d:%02d\x030\n",(gmtime($end-$start))[2,1,0]);
}
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Also, it's a bit out of date, but you might want to read my Test::Class tutorial. It's in five parts, but it's worth the effort.