If you've seen the `on' delimiter, set a flag that you should be printing. Set the flag apropriately whenever a delimiter is encountered. You might also consider Mail::Folder or Mail::Box.

my $printing;
while( <INPUT> ) {
  if( /^From (\w+)/ ) {
    if( $1 eq 'mailsnarf' ) {
      $printing = 1;
    } else {
      $printing = undef;
    }
  }

  print if $printing;
}
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