Keeping a Magic Mouse 2 paired to 2 MacBook Pros

My setup: I have an Asus monitor that I connect to 2 different MacBook Pros. I do NOT use both MacBooks at the same time, but I do switch back and forth throughout my workday. Let me clarify, I do not keep both MacBooks open and running at the same time. One is open while the other is "sleeping".

My problem: I have my Magic Mouse 2 successfully paired to both MacBooks, but it doesn't recognize the connection when I switch MacBooks. I have to go through a multi-step process every time I switch and it is a hassle.

The process: Switch out MacBooks (put one to sleep while using the other). Turn off Magic Mouse 2, turn off bluetooth on MacBook. Turn on Magic Mouse 2, turn on bluetooth on MacBook. Connect to Magic Mouse 2.

There has got to be a way to be able to just switch out my MacBooks by closing one and opening the other so that both machines are never open at the same time and keeping that bluetooth mouse connection without doing "the process" 10 times a day. Again, I'm not trying to use the mouse with both MacBooks at the same time, just keeping that connection while switching between machines.