this is a very good list of items that can help establish that you're no longer a NYS resident for tax purposes, while it only speaks of moving to other states, it's equally applicable to moving overseas:
If you become a full-time resident of Thailand, you're no longer a resident of NYS and do NOT have to pay NYS tax (you may eventually be asked to prove that you live in Thailand, but as long as you can have bills/statements in your name sent to you, and provide a copy of your passport stamps and Visa/renewals, you will be fine).
Evidence of using a Thai bank account, and using a credit card within Thailand is also good evidence of being a resident of Thailand, as well as receipts from medical appointments, etc.
And yes, I still keep a mailing address in NYS (with a relative).
You can also still be registered to vote in NY, but don't vote in any local (city/state) elections, or that will be considered as evidence towards residence in NYS.
Some policies will cover you overseas, but even if they do, you will have to pay up front in Thailand, and then apply for reimbursement from the insurance company.
If most of your income is from investments that's true, but if the majority is from Social Security or a government pension, the DTA excludes those from being taxed by Thailand, and considering that you get a credit for the total US taxes paid, many people would wind up not owing any Thai taxes.
If you're from the US, the DTA specifically excludes Social Security and any other governmental (i.e. state or local) pension from taxation by your country of residence. So if your main income is from Social Security and/or a governmental pension, and that's the money you're transferring to Thailand, conceivably you don't owe any taxes in Thailand.