@stephan - I attempted both of your tests.
- First, with the wire unplugged/key on: The gauge does stay to the left (as it has been doing when plugged in as well).
- Next, I grounded the wire to the block. (At least I think I did. Had some small solid copper Radio Shack wire that I could wedge into the plug, then hooked the other end to bare metal near the exhaust manifold.) With the key on, the gauge DID NOT peg out as you suggested it would. So...if I performed this correctly, it may not be the sensor, but the gauge itself? That would be a bummer.
I'm not 100% sure I grounded the wire properly. I feel the need to try again tomorrow in the daytime!
And just to clarify - when you say with the key "on," you do mean just in the on position, not all the way to the starting position, right? Because whether the wire was plugged in or not, the gauge will still peg out all the way to the right just while starting the engine.
@Revredneck - I am not really sure if the engine is warming up "properly." I know it gets really hot after awhile! I have not checked the thermostat. To be honest, I don't remember how to - the last time I changed a thermostat in a car was about 15 or so years ago in my '87 Cougar! I'll have to read up in my Haynes manual to refresh my memory.

The only scan tool I have is for
ODBII, and this Suburban is from several years before that came around. Are there scan tools that would work with the '92 that can give me the actaul readings from this sensor that I could check? That would be more than my Actron OBDII scan tool (several years old) does for me now with the newer cars!
Thank you both for your replies. I will try to work on this problem some more tomorrow.