Why? In Perl you can use an array to efficiently insert and remove elements from anywhere in a list and trivially reverse it if you wish. In fact the easiest way to handle your problem is to convert between a Perl list and a linked list:

use strict;
use warnings;
use Data::Dumper;

my $forwardList = buildList(1 .. 4);
my $reverseList = buildList(reverse getList($forwardList));

print join (', ', getList($forwardList)), "\n";;
print join (', ', getList($reverseList)), "\n";;


sub buildList {
    my @elements = @_;
    my $head = {data => undef, next => undef};
    my $next = $head;
    
    for my $element (@elements) {
        $next->{data} = $element;
        $next->{next} = {data => undef, next => undef};
        $next = $next->{next};
    }
    
    return $head;
}


sub getList {
    my ($head) = @_;
    my @data;
    
    while ($head) {
        last if !defined $head->{next};
        push @data, $head->{data};
        $head = $head->{next};
    }
    
    return @data;
}
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Prints:

1, 2, 3, 4
4, 3, 2, 1
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