Here's a pure regex solution that works:

use strict;
use warnings;

while(<DATA>) {
  print "$_---\n";
  my $m;
  while (/([QGYN]{2}   # First two characters of the desired class
          (?:          # Followed by the complex expression...
            # Lookback at the previous two chars
            (?<=(.)(.))
            # Check that the next char differs from at least one of th
+em
            (?:(?!\2)|(?!\3))
            [QGYN]     # Then take another of the desired class
          ){1,4}       # ...1 to 4 times
          )/gx) {
    $m = $1;
    printf "---> $m starting at %d\n", pos($_)-length($m);
  }
  print "=====\n";
}

__DATA__
QYGNGNG
GGGGGNYGNQYNNNQGYQ
QGYNNN
xxxxxxxGNNNxxxxxxxNNNGYGYxxxxxxxGYGYNNNxxxxxxxNNNGNNNxxxxxxx
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