Alastair ********************
You will not pay tax if you are in Thailand for less than 180 days per tax/calendar year (unsure of which applies).
Savings, if that's what you will be living on is not income, a pension or rent from a property however is an income. If you have an income it is subject to income tax usually within the country in which it is sourced, in your case Australia.
Thailand has "double tax treaties" with 60 countries which includes Australia, therefore if tax has been paid in Australia you won't be taxed again on the same income.
To pay tax in Thailand an individual would need to be registered as a tax resident, how that's accomplished I'm unsure but a degree of permancy would be required for this to be progressed.
There are a couple of interesting articles which provide an overview of this matter and I'll include them below. I hope they help answer or assist you in some way.
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