Car only starts when I bypass the starter fuse/relay

It does not crank when I turn the key. If I hook up jumper cables same thing, no crank. I went through tests to see what it may be (and had help going through some of this with some guys on ifixit. Com.) Using a multi-meter, I checked the basics to see if I had solid connections. I verified the solenoid, the starter, the alternator, the battery, the battery cables and etc. I then started to take a look at the fuses. They all seem to look fine (nothing appears burnt out). Somewhere in the starting system there is a disconnect. I decided to dive more into the starter fuse/relay. I removed the starter fuse/relay from the fuse box. I decided to ground the terminals in which the fuse is placed. I tried this and was able to bypass the starter fuse/relay and the car started. I went ahead and got a new fuse/relay and when I put it in, the same thing happened. The car doesn’t crank at all. Knowing the old Fuse appeared to look in good shape, and a new one made no difference I ruled that out as the problem. My next thought was it is the neutral safety switch, if not possibly the ignition switch.
I am assuming that since bypassing the relay, the vehicle is not getting positive voltage to the coil side of the relay. I learned if the neutral safety switch does not think I am in either park or neutral, it will not send power to the relay. With that being said, I went to try and ground the NSS. My hope was with the starter fuse/relay back in the vehicle, I could bypass the NSS and get the vehicle to start. My hope was to narrow down that the NSS was the problem. I was not sure which wire contacts to jump for the NSS so I tried three combos for grounding the wires, all with no luck.
I was able to get the car to turn over and try to start (the battery has been sitting for awhile at this point and needs charged) by a combination of grounding the relay fuse (like I referred to in the beginning of this post) as well as the first way I tried grounding the NSS (the first picture of me grounding the NSS connection at the bottom, everything else I did is also pictured).
With that being said, it makes me assume the way I grounded the NSS was correct that time because the car did turn over when I grounded the starter fuse/relay (so there clearly was a full connection through the starter system).
At this point I am fairly stumped. The fuse itself does not seem to have been the problem, it appears to be in good shape and a brand new one did not help. Grounding the NSS without any luck makes me think it was not the problem. If it had been, grounding it should have let the starter relay act correctly and start the vehicle (which was not the case.) What else could be the problem? I am assuming something is keeping the relay from getting voltage to its coil side. What are your thoughts? Thanks!