What is the proper etiquette for posting geisha pictures on tumblr?

Well, that depends on whether the images belong to you or not.

If you took them then that’s fine. However, if you took your images a bit too close to them and didn’t respect their personal space or if they were with a customer then don’t post them.

If you didn’t take them then check with the original photographer first if it’s okay to share their images. If you don’t know who the original photographer is then do a backwards Google Images search or just try to link hop until someone actually gave correct credit where credit’s due. If you can’t find the original photographer then don’t share them. If you have found the original photographer and there’s no restriction on sharing then post it onto your Tumblr and make sure to provide a direct link back to the original source (with photographer’s name) in the description.