I like the idea of processing the data (file) line-by-line, but I would parse the data records to a structure, an array of arrays of lines in which each top-level array element is a "chunk." Once you have the data parsed into a structure, you can do what you want with it.

Win8 Strawberry 5.8.9.5 (32)  Fri 04/02/2021 20:38:05
C:\@Work\Perl\monks
>perl

use strict;
use warnings;
use autodie;

use Data::Dump qw(dd);

my $test_data = <<'EOD';
GO:0002366     False
GO:0002446     True
GO:0002275     True
GO:0043312     True
GO:0006733     False
GO:0019674     False
GO:0043588     False
GO:0055065     False
GO:0055080     True
EOD

use constant {
    'TRUE'  => 'True',
    'FALSE' => 'False',
    };

my $rx_tf = qr{ \Q${ \TRUE }\E | \Q${ \FALSE }\E }xms;
print "\$rx_tf $rx_tf \n";  # for debug

open my $fh, '<', \$test_data;

my @chunks;
my $i_chunk = -1;

while (my $record = <$fh>) {

    chomp $record;

    my $got_tf_rec =  # true if record is valid
    my ($tf) =        # extracted true/false field
    $record =~ m{ \A GO: \d{7} \s+ ($rx_tf) \Z }xms;

    die "bad t/f record: '$record'" if not $got_tf_rec;

    die "first t/f record not false: '$record'"
        if @chunks == 0 && $tf ne FALSE;

    ++$i_chunk if $tf eq FALSE;

    push @{ $chunks[ $i_chunk ] }, $record;

    }

dd \@chunks;

close $fh;

exit;

^Z
$rx_tf (?msx-i: True | False )
[
  [
    "GO:0002366     False",
    "GO:0002446     True",
    "GO:0002275     True",
    "GO:0043312     True",
  ],
  ["GO:0006733     False"],
  ["GO:0019674     False"],
  ["GO:0043588     False"],
  ["GO:0055065     False", "GO:0055080     True"],
]
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