Windows moving randomly

For testing purposes temporarily turn off that original MTP. Press and hold the power button on the right side. Its LED will illuminate then extinguish about five seconds later. Release the power button. Use the built-in trackpad long enough to determine if the same problems manifest or not.

Turn on the MTP the same way. Press and hold the power button until its LED illuminates, then release the power button. It should automatically reconnect. If you experience trouble reconnecting the MTP please write back because the procedure is unintuitive.

The reason for suspecting it may be a factor is that Apple has little or no interest in evaluating compatibility with older devices. Same goes for the Magic Mouse. If it is the same vintage as the MTP they are both about a decade old. Of course they should still work, but Apple gradually becomes disinterested in supporting older devices.

It took some research but please review this old Apple Support document: If your pointer is jumpy when you use a trackpad, Magic Trackpad, or Magic Mouse - Apple Support (Archived).

I do not know the reason it was removed. The recommendations in it are sound, with the possible exception of its recommendation to use a Teflon appliqué, which seems dubious to me. I can personally verify that third party power adapters can be a causal factor. Determine if the problem exists only while your portable Macs are connected to a power adapter (genuine Apple or not) and subsides when unplugged. If it does that would be definitive.

Other factors such as skin chemistry can also cause bizarre problems. Or perhaps it involves the use of hand cream or soaps or even perfume, which that archived Apple Support document may have described as "oils or lotions". For example I strongly suspect that's one reason some people have such awful experiences with Apple's white USB and power cords while mine remain pristine and intact even after a decade of daily use.

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Thanks for following up. I haven't neglected to address your concern. Although I do have a Magic Mouse, it's the original one with replaceable batteries. I haven't attempted to duplicate what you're experiencing with it yet. Unfortunately I do not have a Magic Mouse 2 to test.

The good news is that your MM2 is current production and "supported" while my original Magic Mouse is probably considered obsolete.

For now please review Resolve Wi-Fi and Bluetooth issues caused by wireless interference - Apple Support. Its suggestions may be little more than perfunctory though. If I come up with anything else I will let you know.