Can you obtain a driving license and yellow book in Thailand on a Tourist Visa?

I got a yellow book in tourist visa with my wife address in Thailand

There can be 2-3 month waitingtime for a appointment to driving test.

What is the yellow book please ?

It depends on where you are. Some amphurs are impossible for foreigner to get a yellow book and other very easy. In general though, it's fairly hard to get.

No, on the yellow book unless you have a long term visa.

You can get a driver's license on a tourist visa. You just need to make sure that your immigration office issued residence certificates to people on a tourist visa first, because that's one of the requirements for a drivers license. For example in Bangkok you cannot get a residence certificate while you're on a tourist visa.

Do note that you'll never be able to get a 5 year drivers license on a tourist visa. The first license is always the 2 year license, but at renewal time you'll be issued another 2 years if you don't have a long-term visa/extension.