Man that's a weird and rather loud noise. Given that you say it's on the driver's side it might be the FCV (flow control valve) motor which does, apparently, run a bit after shutdown but why it would make such a loud noise I don't know. Take the cosmetic plastic engine cover off so you can quickly access the FCV (where the driver's side CAC hose attaches to the engine) and the next time it makes the noise see if that's where it's coming from. As loud as the noise is you may even be able to feel vibration by touching the FCV housing. I know you can disable the FCV, harmlessly, by removal of the flapper (2 small screw/bolts I think) but I don't know if you can disable it by unplugging the wiring.
If it is the FCV I'd suggest, since you already have a GDE tune, that you remove the whole worthless mess with one of Week's kits, see
viewtopic.php?f=5&t=78238