I called up Casio Parts and also Pac Parts, and neither were helpful. I asked them if they sell battery clips separately, and they couldn't tell me. I gave them a recent watch model number as an example and they couldn't find anything listed in parts as a battery clip. So... looks like this is something that is considered as part of the module, not sold separately.
The trouble is, I have a Casio watch with a missing battery clip and need a replacement. I checked a few parts watches as donors, but none of them fit. Any suggestions as to what might be a good substitute?