You could have a bad ground at the shifter G303 which is under the passenger's seat but if that is okay you can try putting power to the vio/white wire to see if the gear shifter lights start working, if so, it sounds like the BCM is going out but to be sure we should do a CAN scan which is easy. You can get a CAN scanner (Controller Area Network) from Amazon from about $32.00.
Here is a video to show you how:
https://youtu.be/u-4syLc-ifQ
and
https://www.2carpros.com/articles/can-scan-controller-area-network-easy
Amazon CAN scanner link:
https://amzn.to/3sX8MCX
Here are the gear shift light wiring diagrams so you can see how the system works and I have included how to change out the BCM as well in case you need them. You can get a rebuilt BCM by searching Google or eBay. Check out the images (below). Please let us know what you find. We are interested to see what it is.
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Monday, November 28th, 2022 AT 10:29 AM