If you pulled the connector on the thermo switch and both fans came on, you have essentially proved out the fan circuit including the relay. If the engine is running hot at that time, the culprit is more than likely the thermoswitch. You can measure the resistance across the terminals..........but, to tell you the truth....the switch is very inexpensive.........less than $30. So, I would just replace it.

The part about your note that is confusing has to do with the temp gauge reading hot while driving at speed. At speed, air flow across the radiator should be more than enough to maintain low coolant temperatures. At speed, the viscous fan is freewheeling and the auxilliary fans should be off.

Overheating all the time is probably a defective thermostat...again, this is an inexpensive part to replace.

As another poster indicated, you could have a plugged radiator, though if you are running an anticorrosive antifreeze........plugged radiators are rare.

In summary, you could have more than one thing wrong.......as did I. When I finally sorted out my overheating problem, I found that the hi and lo speed relays had been reversed, the thermoswitch was bad, and one of the two auxilliary fans was defective!