This may be a dumb question, but how do automatic pet water fountains work?

[AZJonnie]

2. All indoor home-designed ones I've seen while shopping for them require you to fill it's reservoir with water yourself

Ones where you connect it to your water line directly may exist but they're not common from what I've seen. Most homeowners aren't adept at hooking up things to water lines inside their houses aside from a disposal, dish/clothes washer, or ice-maker, devices which most homes are pre-outfitted with lines to connect them too, making it a trivial endeavor.

A larger scale outdoor one would be a different matter but is not what people who aren't raising livestock would generally be looking for.