I like your idea of checking the codes. I didn't even think that the computer might be detecting something that I can't. That will be next on my list.

I just finished testing by jumpering the hot side of the pump directly to the positive side of the battery. This forces the pump on. When I do this, the car runs perfect and the SC never cuts out. I drove it around for 30 minutes after it warmed up this morning and it drives great. As soon as I disconnect the jumper wire to the IC pump, the SC will cut out after three or four hard pulls which engage the super charger (and of course heat up the coolant).

I am 99.9% sure it's the relay, or more specifically the computer not detecting that the water is getting hot and needs to come on. Either way, it's at the relay. The fuse is good, the pump is good, it's something in the computer or relay, so back to your initial suggestion, I am going to check for codes.