I went through this process a couple months ago, because I got tired of going to different banks trying to find one that didn’t require it. The form you need is an affidavit. It can be found here:
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You will also need to schedule an appointment with your embassy. Depending on which country you’re from this can be easy or take some “squealing” to get an appt. When I did mine the US Embassy wasn’t allowing appts, but if you lobby and tell them you need for a bank account and visa, they will grant you one - I had to bitch a bit to get my appt. There is a $50 (USD) fee (US Embassy). I would bring any additional documents you have that are relevant, like WP or ED visa to Bangkok bank as they may or may not ask for it.