I wasn't aware this was an option! It's not exactly what I'm looking for, but it will absolutely save me so much time and trouble if I cannot find the exact solution I'm looking for. Thank you very much!
I use a Wacom Intuos tablet for both the laptop and the desktop, I simply plug it into whichever one I'm using. I don't use a trackpad or mouse for either. The laptop is a HP Envy Notebook, which I just remembered *does* have a touch-screen mode available on default (though I'd had it disabled for years because I didn't want to use my fingers and did not own a proper pen for it, so I forgot about that!).
I am glad to know this isn't a simple "toggle this option on" type of answer that I was missing. I'm glad to know that something like that, outside Photoshop itself, can possibly be activating this behavior. I will look into it!