Very helpful, thanks for sharing. my Onstar on 2011 was causing the 10A fuse to blow. Well, now I took the two wires that you have mentioned and reconnect the white and yellow harness and the fuse was fine. My issue was different which I can't connect the OBD reader and get the codes so this helps. I have read in a different thread that we can disconnect the yellow and purple wires from both yellow and white harness but I haven't tired that since your method served the purpose. I don't know what is exactly functioning in the Onstar but will update when I find out. Thanks again for sharing your experience.
One more thing, other mentioned that the car won't start without the module. I am trying to get the car started but so far, the OBD codes won't read until the module is connected.