@Tim ******
Go to your local Thai Revenue Department. Ask for a Thai Tax ID Card (about the size of a credit card but printed on paper). They may/will ask why you need one. Filing a Thai Personal Income Tax Return (PIT-90) in order to claim a refund of your tax withheld from interest earned from a Thai bank account is a legitimate and sufficient reason to be given a Thai Tax ID Card.
(If you have had tax withheld on interest earned go to your Thai bank and get the Tax Withholding Certificate that documents how much interest you earned and how much tax was withheld (usually 15%). Many people are getting these now from the bank as the tax year just ended in December. If they don't understand what you want ask for an aek-ga-san paa-see (tax document) and show them the entry in your passbook where tax has been withheld. Take this tax withholding certificate with you to visit the Revenue Dept and it will be the perfect answer to the question about why you want a Thai Tax ID Card (to reclaim the tax that was withheld).
They can even help you fill out a Thai Personal Income Tax Return while you wait to reclaim your withheld interest. If so keep a copy as you can use again next year when you update the amounts withheld.
With this Thai Tax ID Card visit your Thai banks and get the number added to the registration of your accounts. Tax will no longer be withheld from your interest earned until you have accrued 20,000 baht interest. Because none is withheld you won't have to file a tax return to reclaim the interest. This only works for regular savings accounts, if you have fixed deposit accounts interest is always withheld on interest earned (at 15%).