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I've got a 2001 7.3 Excursion that has been throwing the same codes for 18 months. The truck has never had a problem starting with temps in the 20's and not plugged in. The codes being thrown are P-0672, P-0674,P-0676,P-0678,P-0683. I've checked all conections to the GPCM and all conections to the valve covers and no corrosion and no chaffing. My question is can I damage anything or have I already damaged something by ignoring these codes. (sorry about spelling) Thanks!!!
I'd guess you've either got a bad GPCM or a short in the wiring related to the driver side. If the truck is starting fine, then you're not hurting anything other than the live of the CEL bulb.
GPCM trucks are set to throw a code with any glow plug or controller issues since it may cause more smoke.
It might smoke more, but would probably still start. Since you're issue seems to be isolated to one side, it sounds as if at least half of your glow plugs are still working properly. With at least 4 working, that would make it start up easier.