Well, I found the 944 fan relay in a box (I don't remember saving it, but I did). Connected the battery with the old 968 relay and the fan started to run again. Switched to the 944 relay (same PN) and the fan stopped. I heat cycled the engine to verify that the 944 fan relay worked as intended and the 944 relay performed well.
Here's the tally: 1) one dead battery upon delivery of the car 6+ years ago, 2) one dead Sears battery 4 years ago, 3) one dead Interstate 3 years ago, 4) one dead Red Top 2 months ago, 5) two themo switches over the past 6+ years, 6) spending an entire Saturday cleaning grounding points (I did this a few years ago), 7) meeting a AAA Club driver several times...
Based upon my experience, I would suggest grabbing a spare Fan Relay if you ever have the chance. It may help in diagnosing a dead battery, cooling issues, etc.
Another member here purchased a fairly low mileage '94 that had a new fan relay already installed in the car. My car has around 31,000 miles, so you can't judge the condition of a fan relay by mileage alone.