Not sure where the signal comes from in modern cars as much of it is electronic.
My guess is a switch that is stuck.
In the 90s and earlier there was a neutral start switch that had the back up light function as well.
Later there was a transmission range switch that told the PCM what gear the transmission was shifted into.
You can get a wiring diagram or shop manual on Ebay that will help. The vehicle is getting close to 15 years old. It is going to need repairs from time to time. You can contract that out to a shop with the repair guides or you can do it yourself.
I have never owned or worked on a MKS, but can easily follow a wiring diagram.
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