Just bought at 2nd hand store. Don't. Know year.

There isn't a second hand store in the world that will see a desk without getting it open to see if it contains anything valuable.
Plus most of them have a box of old skeleton keys around.
Call them and ask for the key. If it's locked now, chances are they are the ones who locked it!

Actually, I have bought several old desks and chests there were locked. And in a couple I found a few things of value, (well paid for the desk) So it does happen.

I went to a few second hand stores and bought a few old desk keys for one, on two others I had a local locksmith come out, he opened it, and ordered me a key.