Electrical Neutral Sensing Switch Not Hooked Up... Confused

Cruising the web researching mustang info as I often do and I come across the NSS. I never knew about this sensor and what do you know, it looks EXACTLY whats hanging from under my car. AND it evidently causes a hanging idle... which I have (slightly). I DO NOT have a code 67 and the car runs great. I am able to dump the codes. I looked under my dash at the clutch pedal and find this mess:


The splices I circled in red were connected at one time (blue wire) but have now been cut. I read somewhere these went to the starter so that it doesn't start if the clutch is not pressed down. That feature works as it should on my car. I suspect that my car should get a code 67 seeing that the NSS is not plugged into my trans. Of course I can not see what is in that port now without removing the trans. This hackery flares up my OCD and I would like to get it cleaned up and functioning, if it is in fact not functioning correctly. It also runs just fine, the idle just hangs a second between shifts... should I just leave well enough alone? Any info or feedback is appreciated. .

Is the other plug at the clutch pedal the one that links the NSS to the computer?

Thanks

Right on, thank you. That’s very helpful. Idk why the starter interupter is so hacked up. But it works so. I also don’t know why the NGS is not connected. Fortunately the car runs well. Is there a trick to getting at the NGS or does the trans need to come out to service it? Thanks

Sorry if I wasn’t clear. Then entire sensor is dangling on the side of the case. Plugged in and all. I’ll try to jump it.. I read another post from years ago when you mentioned installing a fuse to jump it.