Here's a simple version that does what you wanted. It's not very robust however, so you may need to tweak it.

#!/usr/bin/env perl

use 5.010;
use strict; use warnings;

my $in_toc = 1;     # we start off in the Table of Contents
my $in_ch2 = 0;
while (<>) {
    $in_toc = 0 if /^\s*=+\s*$/;
    next if $in_toc;
    $in_ch2 = 0 if /^Chapter 3/;
    say if $in_ch2;
    $in_ch2 = 1 if /^Chapter 2/;
}
[download]

The above doesn't use your "rules", but if you wanted to, you could use a hash to keep track of the chapters from the table of contents and look for those exact chapter titles in the text and/or use length to check the length of the string.