...when, in fact, it hasn't. My TP600x's wireless connection icon keeps claiming that the connection's unavailable, even tho' it's patently false. My pre-move wireless connection was indeed flaky ...

The most common wireless connection methods use either 900MHz or 2.4GHz signals. Here’s a closer look at how each of them work, and which one is suitable for certain applications.

What you need is a wireless mouse. To connect a wireless mouse to your laptop, you'll need to pair it using Bluetooth, or connect it to the bespoke USB receiver it came with.