This afternoon (after a lot of research), I stopped by Harbor Freight and bought the Automatic Compressor drain kit.
I had come across this product on Mike Bullock’s site, and in particular, on his useful docs page (direct link to the .pdf here.)
The assembly on the left goes underneath the compressor, (the auto-drain, towards the top in the picture), tees off from the manual drain (towards the bottom right of the assembly). The tee at the top of the picture gets installed in the unloader line, which provides pressure at compressor start-up and shut-down to the end of the auto-drain. That pressure moves a little diaphragm and valve that then opens a small hole in the auto-drain. You’ll see the final connections later.

Printout of Mike's Guide (it looks like it may actually be copyrighted by someone else. See Mike's page for more info.)
I’m ready to start.
First, I removed the existing petcock.
Needs a little cleaning, if you ask me.
Here’s the new auto-drain (and tee) installed in the bottom of the compressor.
The petcock that come with the autodrain was not as nice my original one, so I installed my original one to the tee. I had to be careful to make sure I had enough clearance when the compressor sits upright. I have about 1/16″.
Then I started running the plastic tubing from the auto-drain.
Then, I stumbled across the part in the directions (both the Harbor Freight directions and the .pdf I had printed out) that mentioned that the kit I had just purchased included the unloader line tee meant for plastic unloader lines. Crap, mine’s copper. I’ll have to run to Lowe’s tomorrow to get a standard compression tee, then finish up. The .pdf notes that if you put the tee too close to the tank fitting, heat can make the plastic tubing get soft. I’m going to lengthen this connection to give me a little more room to work with when installing the tee.
Sorry I didn’t finish. I got called inside to fix a crazy washer. (Wouldn’t drain or spin…grrr.)
January 1 update: I managed to fix the washer, but then had to go on vacation (feel sorry for me?). When I started the tail kit on Dec 30th, I powered up the compressor (still having not connected the plastic unloader line) and the automatic drain assembly leaked. Upon closer inspection, there was a HUGE CRACK in the side of the fitting. I packed it up and exchanged it for a new one at Harbor Freight. The new one should work, once I have some time to install it.