Wow! Great! Amazing! It's no big deal, but it is a big deal!
"All of us is smarter than one of us."
Thank you, BruceF!
I posted this question on two forums. Lots of straight forward advice - unplug/plug. Use a BNC connector. Use a KVM switch, etc. All work to different degrees.
Then BruceF tells me I have the switch I need right in the front of my very own monitor.
That is too cool!
I guess that's why these Forums work.