my $seen_16r_secmove = 0;
my $seen_17b         = 0;
my @buf;
while (<>) {
   if (/^:17B:/) {
      $seen_17b = 1;
      print @buf;
      @buf = $_;
   } elsif ($seen_16r_secmove && $seen_17b && /^:35B:/) {
      print;
   } else {
      $seen_16r_secmove = 1 if /^:16R:SECMOVE$/;
      push @buf, $_;
   }
}

print @buf;
[download]

Or a version that doesn't start buffering before it needs to:

my $seen_16r_secmove = 0;
my $seen_17b         = 0;
my @buf;
while (<>) {
   if (/^:17B:/) {
      $seen_17b = 1;
      print @buf;
      @buf = $_;
      next;
   }

   $active = 1 if /^:16R:SECMOVE$/;

   if (!$seen_17b || $seen_16r_secmove && /^:35B:/) {
      print;
   } else {
      push @buf, $_;
   }
}

print @buf;
[download]

Both handle all of these according to the given specs:

:16R:SECMOVE
:17B:
:35B:

:16R:SECMOVE
:17B:
:35B:
:35B:

:16R:SECMOVE
:35B:
:17B:
:35B:

:17B:
:16R:SECMOVE
:35B:
[download]

Untested.

Update: Simplified.