hi
when i first ran your code, i saw too much output... so i changed the return into an exit 0 and i moved your show ( $stack ) into that if code block...
something like this:

my $tree = {
    top => {
        inetUser => {},
        person => {
            organizationalPerson => {
                managedPerson => {
                    personnel => {},
                },
            },
        },
        application => {
            managedApplication => {},
        },
    },
 };

sub explore
{
    my $node = shift;
    my $target = shift;
    my $stack = shift;

    if( $target eq $stack->[$#stack]) {
        show( $stack );
        exit 0;
    }
    my $kids = scalar keys %$node;
    if ( $kids > 0 )
    {
        for my $key ( keys %$node )
        {
            push @$stack, $key;
            explore( $node->{$key}, $target, $stack, $OK );
            pop @$stack;
        }
    }
}

sub show { print "$_ " for @{$_[0]}; print "\n" }

my $stack;
explore( $tree, 'personnel', []);
[download]

oh yeah, i also removed the last two lines of your, since i had no idea what they do... but as it seems: they were not required ;-)
when you run the above code you really get:

insaniac][r0nin: ~/work/code/perl : perl tree_ldap.pl
top person organizationalPerson managedPerson personnel
[download]

hope this helps a little bit..

Update: also removed the eval ;-)