This should be readily adaptable to your schema of variable names and filenames. Please note, it's not valid for interactive input, so don't use it with <>, just to be safe. If you needed to take input from <> you should remove the eof() test, and instead print to one last file after the while loop expires. If you end up doing that, put your output code into a separate subroutine to avoid code duplication.

my @output;
my $outfile_name = "Outfile0000";


while ( <DATA> ) {
    chomp;
    push @output, $_;
    if( /VECT/ or $. % 12 == 0 or eof(DATA) ) {
        open my $out_fh, '>', $outfile_name++ or die $!;
        say $out_fh $_ for @output;
        @output = ();
        close $out_fh or die $!;
    }
}
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