My trackpad is Magic Trackpad 2 A1535. From the thread you cited, it looks like the success others is having is only for the Magic Trackpad 1 A1339.
If I dont cycle the power on the trackpad, it doesnt enter discovery mode and the other computer will not be able to connect. At this point the trackpad wont connect to the original computer because the BLE will be off based on my experiment above. If I turn the BLE back on on my original computer, it will pair if I trigger the ToothFairy app.