I just wanted to say thank you and that this post was very helpful!
I will say however that I didn't need to remove the battery, trans mount or trans mount bracket to get at the sensor. It looks like you have an aftermarket air intake and filter. On the 2007 production 2.0L that I have, I was able to remove the aircleaner with 2 bolts and then disconnected the air intake hose by loosening the clamp at the throttle. Then I was able to get at the switch. First, I disconnected the wire and checked if it was the switch that was a problem by jumping the connector with a wire and the backing lights worked. So then I used a 7/8 inch deepwell socket and was able to get in under the trans mount and remove and install the switch. No need to take out the battery or the battery tray. I thought this was much simpler.