If it's run the way everything else is, the ECM likely just grounds the lead when EGR is commanded.
Should be pretty easy to test this, with key on, one solenoid wire should have 12V, the opposite wire should NOT have continuity to ground. If it does, it's shorted. Again, this is assuming that is how it is run.
You can probably head over to diy-efi.org (GM-ECM) and look through their info, you may find what you need over there, which would be something like an ECM diagram. 1227747 is your ECM.
Also, the later wiring diagrams have been posted on here, if you search my username as thread starter, with "troubleshooting" as the key word, you'll find my post that should have a wiring manual, etc.