Because the eVisitor is free of charge and granted quickly, people sometimes treat it as a light-touch permission to do whatever they like for 3 months. It is not. It is a visitor visa with conditions, and the conditions are enforced.
Work
You may not work for an Australian employer. Business visitor activities are a different thing from working: attending meetings, negotiating, or going to a conference is generally fine; being paid by an Australian business to do a job is not.
Remote work for an employer outside Australia
Working remotely for your existing employer overseas is a grey area that depends on the specifics, and it is not something a comparison site should rule on for you. If your trip depends on the answer, check with the Department of Home Affairs before you book.
Study
Study is capped at 3 months. A short course is fine; a semester is not. Longer study needs a student visa, applied for before you travel.
Why this matters more than it looks
Breaching a visa condition can lead to cancellation, removal, and an exclusion period of up to 3 years. The cost of getting this wrong is not the fine — it is being unable to return.
Source: Department of Home Affairs — eVisitor (subclass 651)
More on the eVisitor
What is the eVisitor
The eVisitor is a full visitor visa granted electronically to holders of eligible European passports. What it covers and how it differs from the ETA.
How to apply
Applications are made free of charge through ImmiAccount on the Department of Home Affairs website. The order of the steps and the mistakes that cause delays.
Cost
The Australian government charges AUD $0 for the eVisitor: no visa application charge and no service fee. The ETA for other passports costs AUD $20.
What you need
A valid European passport, an email address and about fifteen minutes. No photo, no payment, no documents to upload for most applicants.
Processing time
Most eVisitor applications are decided automatically within a day. What causes an application to take weeks instead.
Validity
An eVisitor lasts 12 months from the date of grant, or until your passport expires, and allows as many entries as you like within that period.