If there is question as to the condition of the transfer case (like you just bought the vehicle), I could see that point... otherwise I wouldn't worry about it if it was working prior etc. It is unlikely to have had multiple failures.
As far as the transfer cases go... the shifter operation is your #1 indicator of condition; if it moves solidly between ranges, that is what you want. You don't want it too smooth (the shifter bushings fail and this happens, as well as forks bend and this happens), nor do you want harsh obstructions when shifting of course. The second indicator is noise while driving... and this will about always be heard in 2WD as well.
For 4WD to work you will have the following conditions:
Shifter goes to a 4WD range, 4WD engage switch closes and grounds ecu.
4WD light begins flashing.
Ecu sends 12V to the two front axle solenoids (free wheel clutch solenoid pack) on pin 7 (blue/white stripe).
Solenoids reverse flow and vacuum switches from pulling the front axle out of 4WD to pulling the front axle into 4WD.
Front axle detection switch changes position from 2WD to 4WD (or reverse of course), signal from front axle switch shows a matching position to 4WD engage switch.
Light goes solid indicating 4WD engaged.
AWD versus 4WD depends on your model. The easy way to tell is looking at the shift lever. If you have traditional 4WD it will show 4H-4L-2H. If you have AWD it will show 4H-4L-AWD. The AWD models all have a beefy shift knob; 4WD models some have a beefy shift knob others have a small rubber molded knob.
AWD models use a viscous coupler not found on 4WD models.
Don't worry about pin 6... pin 2 not grounding is where you are worried about. I would be checking the wiring for issues, and if nothing surprising is found, replace that 4WD detection switch.