if(/^HEADER(.*?)GENRE_BY(.*)/
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isn't a regex.

You left out the close paren (for the "if" condition) that was in the OP, but apart from that, it is a regex. It is doing a match on $_, which is a normal and sensible thing to do.

#!/usr/bin/perl

use strict;
use warnings;
our ($fileIn, $fileOut);

use Getopt::Long;

GetOptions(
     'FileIn=s' => \$fileIn,
     'FileOut=s' => \$fileOut,
  );

if($fileIn && $fileOut) {
   open(INPUT,"<","$fileIn");
   #undef $/;
   while(<INPUT>) {
   next if /^\n/;
   s/\t+//g;
   s/^\s+//g;
   if(/^HEADER(.*?)^GENRE_BY(.*)/sm) {
    print ;
   }
  }
 }
[download]

HEADER(
   LIBDAT("GTASK")
   VENDOR("DeltaQ")
   Environment("zeronom")
   TASK_VERSION("5.2")
   GENRE_BY("dumpTc")
)
...
...
HEADER(
   LIBDAT("GTASK")
   VENDOR("DeltaQ")
   Environment("zeronom")
   TASK_VERSION("5.2")
   GENERATED_BY("dumpTc")
)
...
...
HEADER(
   LIBDAT("GTASK")
   VENDOR("DeltaQ")
   Environment("zeronom")
   TASK_VERSION("5.2.1")
   GENRE_BY("dumpTc")
)
...
...
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Your (main) problem is that you're matching against individual lines, i.e. 'HEADER(', next '  LIBDAT("GTASK")', and so on. In other words, the regex can never find 'HEADER...' and 'GENRE_BY...' at the same time.

One way around this would be to split the input appropriately (as shown in the snippet by GrandFather). Another way would be to use the flip-flop operator .. to accumulate the necessary lines as shown below. The expression if (/^HEADER/ .. /^\)/) is true starting with a line matching /^HEADER/ up until a line matching /^\)/, in which case you append the current line to the accumulator ($entry). Upon the next line (not being HEADER or )) the flip-flop is reset to false.

(I've put in an additional end-of-entry test (if (/^\)), so the code will correctly deal with the case where a new HEADER line is immediately following a previous entry (without any other lines in between) — if your input always has other stuff in between the entries, you could also just put the regex test directly in an else branch of the flip-flop test...)

#!/usr/bin/perl

use strict;
use warnings;

use Getopt::Long;

GetOptions(
     'FileIn=s'  => \my $fileIn,
     'FileOut=s' => \my $fileOut,
  );

if ($fileIn && $fileOut) {
    open(INPUT,"<","$fileIn");

    my $entry = "";
    while (<INPUT>) {
        next if /^\n/;
        
        if (/^HEADER/ .. /^\)/) {  # flip-flop
            $entry .= $_;          # accumulate input
        }
        if (/^\)/) {               # end of entry
            # check for desired type of entry
            if ($entry =~ /^HEADER(.*?)^\s*GENRE_BY(.*)/sm) {
                print $entry;
            }
            $entry = "";           # reset accumulator
        }
    }
}
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