Like choroba, I'm wondering: What's supposed to happen to the dash in the 4th position in the second string?
    A-C-G--CTGGC
       ^ dash in 4th position

Assuming it should be replaced by  $tag because it's between the quantified groups of bases, here's a multi-regex solution. (Warning: Needs Perl version 5.10+ for the  \K regex operator — but I can get around that fairly easily if needed.)

c:\@Work\Perl>perl -wMstrict -le
"use 5.010;
 ;;
 use Test::More 'no_plan';
 use Test::NoWarnings;
 ;;
 my $tag = '___';
 ;;
 VECTOR:
 for my $ar_vector (
   [ qw(ATCGGATCTGGC  AT___CGGA___TCTGGC) ],
   [ qw(A-C-G--CTGGC  A-C___G--CTG___GC) ],
   ) {
   if (! ref $ar_vector) {
     note $ar_vector;
     next VECTOR;
     }
   ;;
   my ($seq, $expected) = @$ar_vector;
   my $got = xform($seq);
   is $got, $expected, qq{'$seq' -> '$expected'};
   }
 ;;
 done_testing;
 ;;
 sub xform {
   my ($s) = @_;
   ;;
   my $u = qr{ [ATGC] -*? }xms;
   ;;
   $s =~ s{ $u{2} \K -* }{$tag}xms;
   $s =~ s{ $u{4} \K -* }{$tag}xms;
   return $s;
   }
"
ok 1 - 'ATCGGATCTGGC' -> 'AT___CGGA___TCTGGC'
ok 2 - 'A-C-G--CTGGC' -> 'A-C___G--CTG___GC'
1..2
ok 3 - no warnings
1..3
[download]

Of course, more test cases are highly encouraged!

Update: And yes, this does seem like an XY Problem.

Update 2: Here's the pre-5.10 (no \K) version of the code (tested):
    $s =~ s{ ($bu{2}) -* }{$1$tag}xms;
    $s =~ s{ ($bu{4}) -* }{$1$tag}xms;
And versions, also tested, consolidating the two substitutions in a for-loop:
    $s =~ s{  (?:$bu){$_} \K -* }   {$tag}xms for 2, 4;  # 5.10+
    $s =~ s{ ((?:$bu){$_})   -* } {$1$tag}xms for 2, 4;  # pre-5.10
In all these variations,
    my $bu = qr{ [ATGC] -*? }xms;