Hey everyone, my solution works for me and it's very simple - could be worth trying before anything risky or complicated.
All I do is go to Activity Monitor, choose Finder -> Quit -> Force Quit. Finder re-launches automatically immediately, and my external drives all show up and behave themselves. The same simple solution also works when trash emptying gets stuck. I often find it's the Finder, not the devices and system, that is at fault.