Put one monitor of a dual monitor windows system into standby
This probably isn't what you want, but a potential hackish solution is to hook your monitor up via a KVM switch and simply switch the video input to an inactive input. KVM switches tend to be designed for higher cycles than power switches, and if needed, you could always replace the switch assembly with one you know is rated for millions of cycles.
To the computer/Windows, it will be as if the monitor were turned off or unplugged. With no signal being received, the monitor should put itself in sleep mode.
Otherwise,find or write an ACPI tool that lets you manually send ACPI signals to devices. This might be a potential starting point.
I found a couple of answers to this Question (Turn off display in Windows on command) to be close to what I was thinking of.
The only issue with these is they don't describe how to automate this process, it gives you the ability to sleep a single monitor upon running a script as well as how to turn it back on, but it doesn't tell you how to make all of this happen on the events that you describe.
This site (Turn off LCD) talks about creating a program that makes use of System.Runtime.InteropServices I imagine that you could create a windows service that will sleep one of the monitors upon inactivity and then awaken it when there are mouse events.
If I were tasked with this I think that I could make it happen.