Well, all I was trying to do was be able to see who is connected to my network and when, using the Sidebar as identification.
After failing with the (much appreciated) suggestions, I have (sort of) figured it out!
I sometimes explore preferences and settings, from time to time.
I like to click buttons, hoping to figure out what they do.
So I have narrowed it down to two things…

1. Under Finder Preferences, I re-checked the Devices/(Show) Computer.
2. System Preferences/Sharing/Options, I re-checked the Share files using FTP and Share files using SMB.

Lo, and behold, the Sidebar is now showing my Shared connections.

NEXT QUESTION!

If I can see them, they can see me, right?
If they can see me, do they have access to my computer?
When I click on their icon, it says that the connection failed. That's fine.
I just want to make sure they can't connect to my computer without me knowing it.

Thanks again for the replies.