Yes, both fans should cycle in test mode. I would use a test light or multimeter to backpin the fan connector while in test mode and see if it's getting power. Might just be a failed fan.
The fans really only make a difference under 15-20mph. So with those symptoms, I would question the gauge reading. Might be worth plugging a code reader in and seeing what temp the ECU sees (separate sensor), and/or using an infrared thermometer to test.
Might be a grounding issue causing both problems....