The levers control the air doors inside the mixing chamber used by GM for climate control. The fans speed switch is huge because it has three sets of resistors that drop the voltage to the fan to control the fan's speed. You can check the fan's operation by grounding the case with a cable back to the negative terminal of the battery, and hot wiring the lug on top of the fan with a second cable (that contains an in-line fuse rated at thirty Amps) to see if the motor spins.
DC motors will draw infinite current if the rotor is locked (dead short) so a fuse is needed in this test. DC motors speed is controlled by the voltage applied and the direction of rotation by the polarity (reversing positive and negative).
The aftermarket sells reproduction fan speed switches, but the cables used only come in predetermined lengths so you may have to buy one that is overly long to replace one you can not use.