OP, it's been well debated in the Australia Forum Pension thread.
Article 18 and Article 19 of the Australia / Thailand DTA deal with pensions.
Article 18 relies on the "provisions" of Article 19, and Article 19 deals with "Government Service Pensions."
A Centerlink old age pension IS NOT a government service pension. A government service pension is a pension public service, such as a military pension etc.
Therefore, a Centerlink old age pension is not covered by the DTA.
That said, paying tax in Thailand, if any, could be the least of your problems.
There are proposed changes to Australia's tax residency laws. It's all over the internet. Here's just one link from a private firm.
https://hlb.com.au/tax-residency-changes-for-individuals/
You will note that Australia is moving from a "domiciled" residency model to a physical presence and time based model, the same as Thailand.
For Australia, when these laws are passed, it will be 183 days inside / outside Australia.
The pension is deemed an income.
The pension is taxable.
If you are outside of Australia for more than 183 days in a financial year you will be deemed a non resident for tax purposes. Immigration records will prove the ATO's case.
There are no exemptions, means testing, or changes to the non resident tax free thresholds mentioned in the proposed changes. So the pension doesn't get a free pass.
Non resident tax starts at $0 to $135,000 and is 30%.
As a non resident you do not get the benefit of the tax free threshold. Tax is paid from the first dollar.
If you are wondering which political party supports these changes, both do. A former Liberal government proposed them, and the current Labor government did not bin them.
So, it's when, not if.
https://www.afr.com/policy/tax-and-super/assistant-treasurer-flags-new-tax-residency-rules-20220826-p5bd1v
You are concerned about maybe paying a few thousand baht tax in Thailand, but perhaps you should be more concerned having thousands of AUD withheld from your pension in the future.
Remember, the pension payer, Centerlink (government) is also the pension taxer, ATO (government) and they will know you are outside of Australia for more than 183 days, Immigration (government).
The system is already in place to cut off supplements to pensions when outside of Australia after 6 weeks. It's not much effort for them to tweak that system and withhold 30% of your pension after 183 days outside of Australia.
I would suggest, Thailand tax is the least of your problems going forward.