So I actually might have come up with a way to accomplish this - at least somewhat.

You can open each separate guest/remote monitor in a separate window on your host/local computer (at least on a PC).  When you are on a regular local application, you can use ALT-TAB to switch between windows, but trying to do this when the focus is on a guest/remote window jus sends the ALT-TAB command to the guest/remote computer.  

But, you can use CTRL+ALT+TAB to bring up the application switcher for the host/local computer, even when the focus is on the guest/remote computer.  This even works with the guest/remote computer is in full-screen mode.

The slight downside is that when using ALT+TAB, you just hold down ALT and click TAB multiple times until you hit the right window, and then release the keys and that window is now shown.  With CTRL+ALT+TAB, you can still use TAB to cycle through windows, but releasing the keys doesn't change to the selected window - you then have to hit ENTER.

Hope this helps, but I still would like to see an actual keyboard shortcut to do this easier.  

While it is understandable to err on the side of caution about removing data from guest machines, I still think this is an important security feature that should be implemented in some manner so that all clipboard history (maybe with the exception of pinned items) on the guest machine can be cleared upon disconnect.  Maybe set it up as an advanced configuration editor customization that needs to be enabled, but having this would be helpful to avoid leaving unintended info in the guest's clipboard when the host disconnects.  

I can't believe this hasn't been implemented yet considering how big of a security risk it is to not clear the clipboard history on the guest side, thereby leading to possible instances of guests gaining access to sensitive information inadvertently.  I always try and remember to clear the guest clipboard, but this should be done automatically.  Update on this????  Let's focus on some of these important security features and not aesthetic features...

Update??????

Would be really nice to get some update on this feature request...but I'm not holding my breath...

This is a security issue so it should definitely be added!  Clearing the clipboard history in it's entirety on disconnect is critical so that passwords and other sensitive info isn't accidentally left on remote computer.

Any word on this?  Could be EXTREMELY useful considering everyone globally is working from home recently due to the COVID-19 pandemic.  

Would be nice if Connectwise could actually respond...

Would be nice to get a response from Connectwise...

What is the status of this?  Just tried it on iOS 13.3 and Bluetooth keyboard wouldn't send any keystrokes to remote computer at all.  Please advise.