I've worked on these trucks for many years now and I can honestly say I've never see this but with that said I think if your getting 12 volts to the EGR when the harness is unplugged you have a short to voltage somewhere. You should only get about 5 volts when read with the voltmeter, however I'm not 100% sure on this. You might want to read this article, it is the only thing I can find that somewhat explains how to go about tracking it down. I'll keep looking to see what else I can find but I hope this helps.
http://www.obd-codes.com/p0405
I've worked on these trucks for many years now and I can honestly say I've never see this but with that said I think if your getting 12 volts to the EGR when the harness is unplugged you have a short to voltage somewhere. You should only get about 5 volts when read with the voltmeter, however I'm not 100% sure on this. You might want to read this article, it is the only thing I can find that somewhat explains how to go about tracking it down. I'll keep looking to see what else I can find but I hope this helps. http://www.obd-codes.com/p0405