It is somewhat difficult to understand from your problem statement, so I'll make a few general observations and hope you can take them and run, or clarify.

First, you could indicate what part of the file you are in with a flag, ie,

$meaningless=0;
$alternate=0;
while (<FILE>) {
  if (/MEANINGLESS/) {
    $meaningless=1;
    $alternate=0;
  } elsif (/ALTERNATE/) {
    $meaningless=0;
    $alternate=1;
  }
}
[download]

Next, I am not at all clear on why you need line numbers. A match is a match is a match. If it matches, you can print it, regardless of the line number. You can count line numbers if you combine with the above flag system:

$meaningless_count=0;
$alternate_count=0;
while (<FILE>) {
  #include flags from above
  if ($meaningless) {
    $meaningless_count++;
  } elsif($alternate) {
    $alternate_count++;
  }
}
[download]

Does any of this help?

Scott