Sounds like it could be caused by an anti-virus or backup program.
I have Windows Defender on my system, and no other antivirus. What do you mean by "backup program"? I don't think I have any backup programs installed...
Some sort of drive imaging program that makes a snapshot of your drive periodically (I use Shadow Protect, for example, but here are similar programs from Symantec and Acronis, among others). I don't know how Windows Defender behaves, but it sounds like SOMETHING is looking at your files and changing the modified date stamp.
Is there any way I can test this theory without turning off Windows Defender? (I don't have any drive imaging software installed on my computer, and my computer is free from viruses/malware/etc.)
Try running in Safe Mode for a bit.
Only the program, or should I restart my computer in safe mode?
The computer, or you could run MSConfig and turn off all non-essential startup programs and services. What you are trying to do is see if there is something running in the background that's doing the modification.
I just rebooted in safe mode, and indeed, the problem was fixed. How can I further narrow down what's causing the problem or otherwise permanently resolve the issue?
Time to run MSConfig, turn off all the non-essentials, and then test putting back a group at a time and testing the result. If you get a failure, the problem program/service is in the group you just put back (you can do halves to speed things up, but that's a lot of things to keep track of), so cut that group in half and test each half.
Just to make sure I do it correctly: I open MSConfig, then from the Startup tab, click "Open Task Manager" (I'm running Windows 10). Then I disable all the programs listed under Task Manager tab "Startup". Next, one by one, I enable the programs and test with InDesign to see if there's a problem. Is this correct?
Do I need to reboot my computer and/or InDesign after each time I enable a program? Or can I just disable/enable and then continue working?
Are there any programs that are more suspect than others, i.e. any indication where I should start? I have pretty basic programs in my startup menu:
Adobe Collaboration Synchronizer 15.10
Adobe Creative Cloud (2)
Adobe Creative Cloud
Adobe IPC Broker
Adobe Updater Startup Utility (2)
Adobe GC Client Application
Adobe Updater Startup Utility
Canon IJ Network Scanner Selector EX [my printer]
Canon Quick Menu [my printer]
Dropbox Update (4)
hpwuSchd Application [something from Hewlett-Packard, I think from another wireless printer I've used]
Intel(R) Dynamic Platform and Thermal Framework LPM Policy Service Helper
Java Update Scheduler
NVIDIA Capture Server Proxy
ScanToPCActivationApp [Also from HP]
Send to OneNote Tool
That's it. You do have to restart the computer after every change.
Of the things you have listed, the most suspicious, in my opinion, is the Adobe Collaboration Synchronizer 15.10
Don't forget to check Services, too. You might want to take a look at which ones are running in Safe Mode so you don't have to eliminate them again.
I will be honest and tell you this is time consuming and a real pain...
Indeed, how frustrating. Once I've identified the problem program, what do I do? Uninstall it? What if it's a program that I need? Is there a setting or preference option in InDesign that I can modify?
It's unlikely that there's anything you can do in ID, but you might find some setting in the conflicting program, if you're lucky, that will allow you to exclude .indd files.