[hatzie]

I believe all of the T800 trucks instrument panels are digital using stepper motors to drive the needles... unlike the older rigs with air core analog gauges.
Most if not all of the gauges in the instrument cluster get their information from the PCM over the Class II serial link.

The 2nd design T800 that started in 2003 had problems with the stepper motors in the gauges failing and cracking solder joints on the SMT resistors. There are bunches of videos on repairing them. I'm not sure about the 1st design 99-02 trucks.

You can do lamp and gauge sweep tests using a Tech 2 to figure out whether the gauges and lamps are working then go from there.

You can leave it plugged in. I would. Why do more work than you need to. Torque Pro and a decent quality Bluetooth CAN/OBD II adapter will let you use an Android tablet or phone to display custom gauges. You need to enable the extra GM PIDs. You can get PCM Voltage, Eng Temp, Eng Oil Pressure, Fuel Level, Trans Temp, Tach, Speedometer, and Odometer along with several other pieces of data displayed on a tablet or large phone. All of that data comes out over the J1962 OBD II datalink.