I've leaned on this whole site heavily to purchase my "new" 98 that's in rather fantastic condition for its age (very clean, and only 162K miles at 18 years with minimal rust underneath). The dealer I bought it from had done a bunch of work to it (hoses, belts, water pump, exhaust, tires, battery, wiring, et al) but I've been giving it some TLC, too. The clock thing was one of those things you can just accept from an 18 y/o but I wanted to mend it anyway. Like the OP's wife said, I didn't realize how much I used my in dash clock until I had this vehicle without it functioning!
AAAANYWAY, I signed up for an account just to say THANKS and this worked like a charm!!! I actually went to the local salvage and bought a clock off a scrapped 99 (I think). Tried it, and it also didn't work. So I took my original clock apart, tossed the springs aside, did a crappy soldering job, hooked it into the wiring harness, and bam! It lit right up! I put the whole dash back together and was setting the clock when it went out again.
Suspecting my suspect soldering I went back to the work bench, took apart the salvage clock, did a really NICE soldering job on it's circuit board, put that circuit in my original housing and it's worked perfectly going on a week now!! I put all the non working guts back together in the housing with the scrap yard markings and returned it for my money back! Haha! Score one for the nerds with basic circuit and soldering skills!
A couple of tips: I recommend scratching up the area on the pins where you'll solder them with the corner of a little flat head screwdriver or something, the original finish doesn't want to take the solder really without some abrasion. Also another tip to line them up nicely: get one soldered in just like you want and then use a tiny piece of tape across the top of that and all the rest to hold them in line just like you want. These little things worked like a charm to address the unique little challenges of this particular project.
All in all it was a pretty quick and simple fix!