After some experimentation, and perusing a few forums, I determined that I needed to make my own Repository for the Components I was making, and then set the Repository in the Component Details page (it is "Unknown Repository" by default). You can find detailed information on how to do this here.
I did something slight different though in order to have a single repository for all of my custom components, and have that repository listed in the Component Database Manager, as well as in the "C:\Windows Embedded Data\Repositories" directory.
- Create a new .sld in Component designer
- Right click the Repository tree node and click Add Repository
- Name your repository something appropriate (e.g. "MyRepo" or "ZipCo Custom Components") and set the source to a (pre-created) directory of your choice. The directory should have a text file or something in it marking it as your repository, since it will be given a long, hard to remember GUID for a directory name after step 4.
- Save the .sld and import it into your Component Database. Note: In the import .sld dialog make sure you have the "Copy Repository to root" checkbox checked.
PS - If you see error messages importing your .inf driver file, read this before you assume something went terribly wrong. :-)