Reverse Light Problem

[03whiteTahoeZ71]

So I recently bought 03 tahoe z71. The issue at hand is that my reverse light stay on while in park,reverse,neutral,and drive there upgraded led with with led light. Also second issue at hand, the shifter lever can move without any brake pressure. So basically lever moves freely. Any guesses on what can be the issue thanks for any comments in advanced

 

[Cbncanada]

I suspect it is all related to the damaged shift lever locking system. The reverse light switch should be in there with it.