If you are buying a used bike, it will probably have an insurance sticker on it. This sticker will have the bike brand name and the plate number on it.
The insurance carries over with the bike. Have a Thai read it and tell you when it expires. If no sticker, it is easy to get the insurance, even for a bike with no license plate.
3rd party insurance is 645 baht per year, and covers medical only. No theft or property damage coverage. You have to give them the bike info and an address. They don't care about the license, because the bike is insured, not the driver.
BobS
"The true secret of giving advice is, after you have honestly given it, to be perfectly indifferent whether it is taken or not and never persist in trying to set people right."