That's a good idea. Here is a stab at it using String::Random. The sub generates a string of given length of 0,1,2 and then converts this to character codes that String::Random understands. The sub ensures that no three values in a row are the same.

use String::Random;

my $length = 10;
my $Random = new String::Random;
# add new pattern char for upper and lower case
$Random->{'A'} = [ 'A'..'Z', 'a'..'z' ];
my $pattern = generate_pattern($length);
my $password = $Random->randpattern($pattern);;
say $password;

sub generate_pattern
{
   my $length = shift;
   # populate first two values
   my @chars = ( int(rand(3)), int(rand(3)) );
   for my $i (2..$length-1)
   {
      # check if previous two values match
      if ($chars[$i - 1] == $chars[$i - 2])
      {
         my @other_values = grep( !($_ == $chars[$i - 1]), (0..2));
         # get random other value. ie if last two values were 1, pick 
+0 or 2
         $chars[$i] = $other_values[ int(rand(2)) ];
      }
      else
      {
         $chars[$i] = int(rand(3));
      }
   }
   my $pattern = join '', @chars;
   # convert random string of 0,1,2 to A,n,!
   $pattern =~ tr/012/An!/;
   return $pattern;
}
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Edit: It's a little ugly, but this is quite a bit faster than the route I took in my other code sample above.