You can declare yourself a non resident for tax purposes.. your choice
But you would only do that in a situation where you have overseas income and paying tax in another country and don't want that income also subject to Australian taxation as well.
As long as you are leaving each time before your 60 days expires you will receive another 60 excemption entry each time you enter Thailand.
As long as you have proof of a flight to exit Thailand within 60 days it doesn't matter to the Thai immigration doesn't care where you are going as long as you are leaving the country.
Twice per calendar year is the general rule but as many say on here it's at the discretion of the Immigration officer if you attempt a 3rd time within a year and in most cases you will probably get in ok..
If you are concerned then get a cheap flight to Cambodia or another neighboring country and stay there for a few days and then fly back in and get another 60 days..
Flying in and out seems safer than doing a day run over a border and back again..
The bottom line is this...
If the immigration officer dealing with you on the day you enter Thailand from anywhere (land, air or sea) thinks you are abusing the tourist visa exemption system and living in Thailand and not a genuine tourist then you can be refused entry after more than 2 entries in a year.
But in reality this is unlikely but it's always a risk..