When you're filing in eVisitor (subclass 651) visa, one of the questions is purpose of your stay. You have to choose between "Business" and "Tourist", if you mix both you should select "Business"
If you intend to conduct any business activities on your visit to
Australia, select 'Business'. Business activities may include
attending business related meetings, seminars, conventions,
conferences or networking.
If you intend to visit Australia for holidays, tourism, recreation or
to visit family or friends, select 'Tourism'. 'Tourism' may also
include informal studies or training.
If the purpose of your visit is a combination of business and tourism
as defined above, select 'Business'. (source)
In case of physical paper application that's Form 1419 vs Form 1415.
I'm assuming that you've selected "Tourist", thus rule 8115 doesn't apply to you. You aren't allowed to do even the things mentioned there. What applies to you is:
Visa condition 8101
You must NOT work in Australia.
However, I've found this on UK Expats forum, not sure if of the source of the quote, but it covers exactly the case you're asking about (emphasis mine):
Tourist visa applicants wishing to work online (for example, wanting
to check emails online) should be considered on a case by case basis.
If the applicant is holidaying in Australia for a short period, and
just wishes to keep on top of work back home (that is, the online work
is incidental to their trip), this is not of concern in terms of
condition 8101. An applicant who wishes to continue to work online,
basically full-time may be of concern in terms of the genuine visitor
requirement and should be considered carefully.