I had the same problem, but Adobe had a solution for it.
There is a Keyboard-Shortcut for this. But it is not assignt to
any button on default.
You will find this function under the keybaord-shortcut panel.
It ist named: “Enable Transmit”.
Just add your own shortcut, and activate your second screen.
Now you can toggle it on and off with this shortcut.
PS. In german the name of the shortcut is:
“Übertragung aktivieren”