If the money is already taxed in a country with a double taxation agreement then there is no liability so there is no need for a TIN or tax return.
Extract from the Thailand Dept of Revenue website:
C. Elimination of double taxation
The focus of a DTA is the elimination of double taxation. Each DTA may prescribe different methods of elimination of double taxation of a person by the resident country:
(1) Exemption method
The country of residence does not tax the income which according to the DTA is taxed in the source country.
However, if you are a tax resident and bring untaxed money onshore, earn money in Thailand, or have investments in Thailand, you are obliged to obtain a TIN and file a tax return. Any tax you have paid under a DTA can be used as a credit towards your liability here in Thailand.