Sorry it took so long to get back to you. It looks like it's powered from the Auxillary Junction Box under the hood. It makes a difference on your build date as to how it's wired. If before 9/29/2000, it's powered by fuse # 105 (20A) which is also tied to the hydraulic fan control solenoid. If after that date, then it's powered by fuse # 110 (5A). Early build is a 16 gauge wire that is Green w/yellow and late build is a 20 gauge that is orange w/yellow. I see no relay in the picture...so you must be looking at a short somewhere.
Can someone take a test light to one of their vehicles (I don't have access to my son's right now) for us and see if this fuse (whichever circuit your build date requires) is powered up with the key off? If not, then you know that you are picking up power from somewhere and need to find the short to power. If it is powered with the key off, then it looks like the ECM grounds the circuit and it is probably the culprit. But before I condemned it, I would disconnect the ECM and see if the draw goes away. If it does, then you have a safe bet the ECM is bad. If it doesn't, then you must have a short between the ECM and the IAC motor. This shouldn't be that hard to diagnose knowing what you do now. Fixing it may be a bitch though!! LOL