So did you check to see if the EGR solenoid wiring is good? Unplug the solenoid, see if problem is gone. If the problem doesn't go away, something is wrong with the vacuum line hookup, or the solenoid is faulty, period, since removing vacuum solves the problem.
Not looking at a wiring chart, I assume the EGR solenoid gets a constant 12V with the engine on, and the ECM commands EGR ground when the right conditions are met. No matter how it's wired up, either there will be 12V on one wire, and no path to ground (engine running, idling in park) or no voltage and one ground. I almost guarantee its 12V constant and no ground though. At least that's how it SHOULD be at idle, since EGR only operates at a steady state cruise condition.