Ok... I just got home and I put the meter on it again. I only had 12.02 volts with the engine off and 11.88 with it running.
Now, when I start the car, the Battery light, Brake Pad wear indicator light and E-brake light are not coming on at all? So, it appears that something has had a meltdown.
Where should I start looking? Behind the cluster or under the hood? A bad voltage regulator would not cause this. Right?