Hi there...been browsing a lot of forums and with bits of different snippets here and there I finally solved this problem with all that help. I'm posting the problem here in that it may help someone else troubleshoot their problem faster with a similar truck and return the favor of all you posters out there.

My 2004 Suburban 2500 had the issue that the Rear HVAC was not blowing on selector speed 1, using the front or auxiliary switch. Selector Speed 2 and 3 were both are working fine, from both the front and auxiliary switch.
I confirmed that ALL speeds on the 2004 Suburban 2500 go through the HVAC Blower Motor Resistor including the high speed (3). Other makes/models may have the high speed as a direct, independent circuit into the blower motor.
The faulty resistor readings (ACDELCO Part 15-80564) based on the three-prong outlet, where the left-most prong on the picture =1.
Between 1 and 2 = 255 ohms
Between 2 and 3 = .513 ohms
Between 1 and 3 = .411 ohms ß-----BAD
The good resistor readings
Between 1 and 2 = 254 ohms
Between 2 and 3 = .36 ohms
Between 1 and 3 = 253 ohms. ß-----Good
Hope this helps someone out….