Back-up light switch - electrical connector/wire missing

[TuftsAuto]

Recently, I noticed that my back-up lights were not working. I checked fuses and found that they were good. I also visually inspected the bulbs and they looked good as well. After searching on the forums, I found that the back-up light switch was a likely culprit based on the frequency of posts related to that part failing/becoming dirty.

So based on that, I ordered the switch and jacked up the back end of the car to replace it this afternoon. It was easy to find the switch's location, but I was shocked to find that while there was a switch threaded into my 6 speed transmission, there was no wire connecting it to the car. I searched around and stuck my arm into the underside of the car as far as it would fit to try to find the wire, but to no avail.

A little history on the car: I'm the third owner of a 2002 Boxster S with ~68,000 miles. The first owner experienced the IMS failure at ~45,000 miles. Porsche replaced the engine for him with a remanufactured version. I imagine that in doing so, they forgot to connect that wire. My fear is that the needed wire got trapped somewhere above the transmission when they re-installed the engine in the car.

Does anyone know where this wire comes from? I don't have the time or the space to drop the engine, so that's out of the question for me, but I do need to get the reverse lights working. Thanks for your help.