Ideally, you could modify the scanner's driver and figure this out entirely in software.
People who are more comfortable with hardware, like myself, may try something kind of hacky... In the end, it always depends on what your needs are. You could attempt:
Open the scanner casing and discover how the paper sensor works. This may involve use of an oscilloscope.
Interface something to that sensor, or a line the signal you need is pulsed on - I'd use an Arduino for this, for many reasons - mostly cost and they're easily interfaced to a desktop machine.
Have your computer poll (Scheduled Task in Windows, Cron job on Linux) the microcontroller you added in step 2. The microcontroller will respond in kind when it's observed that the signal was sent. The desktop can then go ahead and do whatever else you need done on that end to manage the scanner. It may just be calling the driver to start a scan.
That's sort of a Rubegoldberg / Jeri Ellsworth solution - which is why I kind of love it. I'll reiterate, obviously you'd find a software-only solution. Though my minor experiences with driver hacking were painful and maybe something like this will get your needs met with fewer tears?