Finding the other end of an ethernet cable that's punched into a 66 Block
Encouraged by the comments to my question, I bought a tone generator and probe (I bought a Fluke). Here are the steps I performed:


I plugged the toner into the jack in the stereo cabinet and set it to generate a tone for the probe.
I took the probe to the equipment closet and set it to the same icon as I had set the toner to.
In the equipment closet, I passed the tip over all the cables coming in from the wall.
The audible signal made it completely obvious which cable was the one I was looking for.
Once I found the cable, I pulled its blue/blue-white pair off the block.
I terminated the cable with an RJ45 keystone jack.
I tested the pins with my little Ideal VDV MultiMedia Tester.
I turned off my laptop Wi-Fi, cabled it into the equipment closet, and googled a word I knew wouldn't be cached. Called it a win when Google returned results.