Dodge: 1995 Lebaron no-start... continued

Hi again, all. I got a chance to look a little more at my sister's 1995
Chrysler Lebaron with 3.0 and AOD tranny. It will not crank using the key
after having the starter replaced at a shop. I am able to get it to start by
jumping the relay connection under the hood. The relay also seems to be in
working order.
Originally we thought the security system wasn't disarming, and that's why
it wasn't starting. But today I was able to set off the alarm and shut it
off by unlocking the driver's door with the key.

But the security light still blinks. Is it supposed to blink when disarmed?

I looked shortly for a neutral-safety switch to wiggle the wires on... I
don't see one on top of the tranny. Where is that located?

I appreciate the help.