Looking at the docs for LWP::UserAgent, we can see:

$ua->redirect_ok( $prospective_request, $response )
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This method is called by request() before it tries to follow a redirection to the request in $response. This should return a TRUE value if this redirection is permissible. The $prospective_request will be the request to be sent if this method returns TRUE.

So basically, you want to create a redirect_ok method that always returns a true value. A clean way of doing that is to create a subclass of WWW::Mechanize that overrides WWW::Mechanize's redirect_ok method.

package WWW::Mechanize::AlwaysRedirect;

# this class is a subclass of WWW::Mechanize
use base 'WWW::Mechanize';

sub redirect_ok {
   1;  # always return true.
}

package main;

my $agent = WWW::Mechanize::AlwaysRedirect->new();

# proceed as per usual with this $agent instead of the one
# in your original code
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You seem to be slightly confused by object-oriented techniques. You should probably take a look at at perltoot and perlmod. There is also the very good "Object Oriented Perl" book by Damian Conway.