EGR problem!!

Hey guys, I'm having a problem with a p0405 code. I believe its called circuit a low voltage. The red wire on the end of the plug has 12 volts when it isn't plugged in, and when I plug it in, it has nothing. I'm thinking this is where my problem is, but still unsure. I changed it to an egr valve that I know is operational, and came up with the same thing. Just to see if that is normal, I compared with my mom's blazer. Appears to be the same setup, but her red wire has 12 volt whether plugged in or not. Also was wondering what the downfall would be of having allen delete the egr. I'm in NY, so I have to pass emissions inspection, but I've heard of people deleting their rear o2 sensors, and still passing.

I also metered all the wires plugged, unplugged, running, and not running.

Red was 0.032 plugged, 12 unplugged not running.
Red was -0.001 plugged, 14.14 unplugged running.

gray was 5.03 plugged or unplugged not running.
gray was 5 plugged or unplugged running.

brown was 0.703 plugged, 0.030 unplugged not running.
brown was 0.670 plugged, -0.003 unplugged running.

purple was 0.032 plugged, 0.031 unplugged not running.
purple was 0.001 plugged, -0.003 unplugged running.

white was 0.032 plugged, 0.031 unplugged not running.
white was 0.001 plugged, -0.003 unplugged running.

I was hoping someone would know what the volts are supposed to be when working properly. Thanks for your help.