I now have a valid Australian visa (Electronic Travel Authority) valid for 12 months, multiple entries, with no one stay longer than 3 months.
Does Australia require proof on onward travel, or do they just trust me not to stay longer than the 3 months?
Usually it's just trust. A friend has travelled to Australia on this visa a few times now and never been asked to show proof of onward travel. There is a new government now though and immigration is a priority so there could be a crackdown on this. Answer: unlikely but vaguely possible. over 4 years ago