You don't need a separate Munchkin tracking code -- there's no such thing. The same Munchkin ID can be used on any number of domains. That's probably why you couldn't find any directions.
But the Munchkin tracking cookies will not be shared across parent registered domains, so this concept is flawed:
we simply want to track activity such as page views from known leads in www.companywebsite.co.nz when they visit www.externalsite.com.
Cookies from .example.co.nz are not sent to example.com -- a core tenet of browser security. Each registered domain thus gets its own cookie, which will be anonymous until the session becomes promoted (from anonymous → known) on that domain, using one of the standard methods (email click, form fillout, Munchkin API or other associateLead method).
An expert client-side developer can bridge this gap (it's the kind of thing we build here) but you shouldn't expect it to work by default.