In addition to the suggestion to use strict;, I recommend you not rely on implicit variables.

#!/usr/bin/perl
#^^^ added / after !

use warnings;

open my $wave,    '>', 'Wave' or die "Can't open $wave: $!";
open my $keywords,    '<', 'Agents' or die "Can't open keywords: $!";
open my $search_file, '<', 'Definitions'   or die "Can't open search f
+ile: $!";

my $keyword_or = join '|', map {chomp;qr/\Q$_\E/} <$keywords>;

close $keywords;

my $regex = qr|\b($keyword_or)\b|;

OUTER:
while (my $line = <$search_file>) {
      # ^^^^^^^ using just $_ is for chodes
    INNER:
    while ($line =~ m/$regex/g) #<~ why is this a "while" an not an "i
+f"?
    {
        # skip if...
        if ( $line =~ m/(?:SCRIPTNAME|DESCRIPTION)/ ) {
                        #^ if you're not capturing $1, don't keep it i
+n memory
          next INNER;
             # ^^^^^ labels when using "nested" loops can be very help
+ful
        }

        print $wave $line;
    }
}
close $wave;
close $search_file;
<code>

Final note, you're opening yourself up to some adversarial input attac
+ks by trusting <code>$keyword_or
[download]

and blindly iterating over $search_files. Idk I think I also found an issue with your next and question your use of that inner while altogether.