How to remove the Safety Neutral Switch?

That is the detent plate. The transmission position sensor goes on the outside of the transmission over the manual shaft. It is already gone in your picture. What is the issue you are having?

Normally yes, they are on the outside, but this one isn’t it’s on the inside of the transmission.
The part is still in there and doesn’t want to come out.

Okay, I think I've found the problem, they used two different transmissions in that car. The 4T45E uses the external switch, you have the 4T65E which has the internal switch. To get that one out you have to remove pretty much all the pieces in the transmission to get room enough that it can be pulled into the case and get the shaft out.
Basically, the entire valve body has to come out then the actual gearing for the transmission and the apply pistons and clutches all need to come out. Pretty much doing a rebuild with it to get that switch out, as such you might want to get a kit and go through it since you will be almost there just getting the switch out. There is a retaining pin that holds it in the case as well. It is pretty much the last thing to come out of the case and the first to go in.
This is a good teardown video on the unit you have. At around the 32-minute mark you can see that the switch and shaft can now come into the case and out.

https://www.youtube.com/watch?v=6b8-8FxNvTc