Owner just need to give you copy passport with signature + copy visa with signature (previous owner still have valid visa, if you said your previous owner visa expired i suggest you to explain to officer at DLT) + form with signature (not sure which form but it can get from DLT, owner have it already and give earlier when they make a deal)
My friend (foreigner) just bought car from foreigner on October 2023
Document he prepared :
1. Original Blue Book
2. CoR (both from embassy / immigration is valid)
3. Form (that i mentioned above)
4. Tax paid (last year 2567)
Go to DLT Chatuchak building B / Building 2 along with all document