At the prompt of a UDN post, I investigated the cooking/staging code and discovered that it is hardcoded to copy files for the "Game" localization target. This needs to be configurable in some manner. Most likely, all targets need to be staged unless any are specified somehow, in which case only those specified should be staged.
Create a localization target that isn't named Game. Cook a build. The build will not contain the localization data for the new localization target.
There's no existing public thread on this issue, so head over toAnswerHub just mention UE-20248 in the post.