I received my new shifter assembly today. I haven't had time to swap it in, but did get a chance to look it over really well. Assuming that the new assembly is similar in design to the old one I can definitely say the problem lies in the assembly base. On the new assembly, the button on the shifter knob actuates a spring loaded mechanical lever, that is it, it has no electrical function. The only wires go to the select shift +/- button. However that lever is connected to a spring loaded plunger that has two wings on it that engage the detents for each position. The park position is guarded by a solenoid actuated gate. I assume it requires the brake signal to actuate the solenoid to release the guard allowing you to move out of park. On the opposite side in the park position, the plunger wing engages a metal flat spring. Above that flat spring there is a tiny push switch. When the shifter button is released, the plunger moves into the detents and in the process pushes that flat spring up which engages the push switch. I am assuming that completes the circuit that powers the dash light as well as the shift to park message.
When I get the other one out I will be able to make a comparison and figure out the root failure that is causing the issue.