Thank you for the reply.
In my case, the behaviour is occurring on a Surface Pro 3 running Windows 10, so the DP output should not be an issue. The USB is directly connected to the dock of the SP3, so, again, that should not be an issue.
The functioning monitor is set to its native resolution of 1920×1080. The non-functioning monitor is set to its native resolution of 1680×1050.
Windows detects the non-functioning monitor with no problem. See attached.
It’s just that no image ever shows up on the second monitor. I’m at a loss.
Here is the Display control panel with the monitor on:
And then with it off: