You might try anyway. Believe I use the thunderbolt connection for my monitor, the second direct hdmi connection is used only for sending ddc commands. In other words, both inputs seem to be listened to with my Dell monitor.
Your monitor must listen to DDC commands from inactive inputs. I think mine doesn't, because this whole problem came about when I realized that my desktop could ask the monitor to switch to the other input, but couldn't ask it to switch back.
Apparently a lot of computer monitors only listen to DDC commands coming from the selected input, while TVs almost always listen to them from all inputs, because they often need to do things like "switch to Roku input when the Roku asks, even if some other set-top box is driving the display."
If my monitor could do this, I could just run the input switching script entirely on my desktop (based on whether the keyboard has just appeared or just disappeared), and I wouldn't have to send DDC commands via the dock at all.
You might try anyway. Believe I use the thunderbolt connection for my monitor, the second direct hdmi connection is used only for sending ddc commands. In other words, both inputs seem to be listened to with my Dell monitor.