I finally found the Dropbox FAQ that explains why I've never been able to use the new Dropbox Backup program on my external drives: "Note: Encrypted APFS drives aren't supported."
Apple recommends encrypting external drives that contain any personal information, and that's obviously for a good reason. Does Dropbox intend to support Encrypted APFS drives at some point? Other backup programs (e.g., Backblaze) have no problem with this.
(And is there any known way to work around this limitation?)
Thanks.