2001 Maxima does this..

its not the cluster, not the shifter, not the brake pedal switch, not the tail lights, ...Any suggestions.

 

There should be a lock out switch in the shifter that keeps it in park until the brake is pressed. It sounds like your issue may be in that circuit.

Will it pull out of park without pressing the brake?

 

You solved it..the lock switch is shorted.

 

Thanks!

 

What an unnecessary part/function (but with most of the population fully retarded, I guess they have to).

 

Good deal. Nothing like an easy fix.
While I agree with it being unnecessary I'd still fix it. People have been trained to think that everything is safe these days. You never know when some curious passenger, maybe even a kid, will play with the shifter.

 

Heaven forbid we check things before doing something. Our nanny state government will make it safe for us.