Thanks to the article's pointer, I finally decided to fix the clock backlight in my '96 LX.
However, I wasn't very handy with a soldering iron (BSEE degree notwithstanding), so I headed down to my local Ford dealer (I needed to pickup some small parts any way).
The clock assembly itself costs abotu $60. However, a quick check of the computer shows that the light bulb can be purchased separately to the tune of $5.75.
So I popped the corner piece off, then slide the clock module out of the dash, and disconnect the socket. I then use a snall socket wrench to turn the bulb to disengage it, put in the new one, reconnect the socket, fit the module back, pop the corner piece back, and adjust the clock.
Total time elapsed: less than five minutes.