Neutral Safety Switch pics please
2nd have you verified the location of the NSS (neutral safety switch) as being under the dash and on top of the steering column, yes?
In the 1st pic the steering column is missing the metal tab coming out of the steering column that moves the spring loaded pin when the gear is changed. So the position of the spring loaded button is in D,L1,L2 and the truck will not start. I bet that is why they cut the wires, but the truck will still not start unless 2 of the 4 wires are connected. The metal tab is snap locked on the the steering column inner shaft.
Now you can see the tab (coming out the steering column tube), when in Park the metal tab is full left, as you move to Reverse the tab moves right one position, (and turns on the reverse lights), N right again, D right again.....
How to adjust the neutral safety switch? - Ford Truck Enthusiasts Forums (ford-trucks.com)
I like the idea in post #3 of that thread ^^^ , one can watch a mirror to see when back up lights light up as they adjust.
Neutral safety switch adjustment - Ford Truck Enthusiasts Forums (ford-trucks.com)
The hole if using a pin: If the tab is present, once adjusted correct to any position, be it 1, 2, 3, N, R, then it's gonna be right in the others. I've never used the pin in the hole myself, loosen two bolts so youi can slide the switch left to right on the column, put truck in 1 first, then set the switch to the neutral position by manually moving the post on the switch to your left to where the locking pin can be inserted, then with gear selector lever moved to neutral, you gently slide the switch to your right until the post touches the tang, snug the bolts, remove the locking pin from switch before throwing truck in park. With your locking pin in the hole, the switch may not* be free to move so think before shifting the lever. The pin inserts on the back side or "mounting bolt" side of the switch. You can use a paper clip or drill rod or even a small Allen wrench or other fitting size rod for the pin, you can even remove the NSS from the column long enough to turn it around to see the hole and set pin in place ... just keep gear lever below reverse as long as the pin is in place. Truck park brake set or wheels chocked.
* Note added here ...
I forget if locking pin blocks switch from any movement ... or ... if it just holds it against the spring in neutral, but it may remain be free to go up through R and into Park ... ? 
Looks like a fair video, shows some good angles too:
On another note, I had taken the steering wheel off to see what all I needed to replace to get the indicator working and I blew the column out with an air compressor as best as I could and it seems to be shifting better.... or that may be in my head... anyways here are pics of my switch in the gears I think they are in..
Maybe it needs minor adjustment since neutral is so far over and not making a connection?
park
reverse
neutral
drive
2
1













