I registered with expatvac on August 10.
I was concerned that I'd heard nothing, so I emailed them.
I got the following reply within an hour.
If you have received your confirmation email, your registration has been approved. You will be sent an appointment details once your vaccine has been allocated by the Ministry of Public Health. At this point, the majority of registrants' info has been sent to each province and to the Ministry of Public Health, and more continue to be forwarded.
The waiting time could vary from group to group and province to province. Normally those in the high priority group are notified within a few weeks.
Please note that each province's vaccination scheme is progressing at a different pace, owing to the different capacity of local medical facilities and the fact that the system prioritises those in the vulnerable groups such as persons aged 60 or over and those with underlying medical conditions first.
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Department of Consular Affairs
Ministry of Foreign Affairs
The Kingdom of Thailand
Make of it what you will.