I have two computers set up next to each other - one Mac and one PC. Is there a mouse out there (Bluetooth, perhaps?) that I can use on both - one computer at a time - without linking the desktops? I'm thinking maybe a mouse that has a side toggle that switches which machine it's hooked up to at any given time. Doable?
Not to my knowledge, SamTheBrand.
But a KVM Switch is going to do exactly that, as well as allowing you to share keyboard and monitor if you so wish. They go for cheap (20 USD and under) on many stores, with more capable ones not going much over 40 or 50 USD.
Computers won't need to participate on a network.
@A Dwarf's answer may work. The only consideration is how close are the two computers? The fact that you stated "without linking the desktops" leads me to believe they aren't right next to each other. There is such as thing as KVM-over-IP. They're expensive, so it may not be the best option for you but you can run them farther. Additionally your keyboard wouldn't be very mobile.
Bluetooth will be your best bet. You can get a receiver for each PC and use the same keyboard on each. The problem with that is it will do the exact same thing on each PC at the same time so you'd have to manually disable it on one of them.