You can buy a vehicle on visa exemption as your visa status itself is largely irrelevant. You will need a certificate of residence from immigration (or in select cases, your Embassy in Thailand may issue one) and some immigration offices may require you to have filed a TM.30 or a 90 day report in order to get the certificate.
You should also keep in mind that you’ll be ineligible for any financing so you’ll have to pay upfront.
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