Ok this diagram is pretty close to what you have ( i couldn't get my laptop up and running). You should be able to disconnect your neutral safety switch and with the key on see if there is 12V on the Purple/orange stripe wire. If you get 12V that means you've eliminated all the wiring up to this point.
Put the truck in reverse and and have the key still on (don't have the engine running obviously and I would suggest to set your ebrake. Then probe the Black/Pink wire to see if you are getting 12V, if you don't then it is your switch.
Now to check for a ground pull out your tail light and locate the socket for your reverse bulb. See if the black wire (solid color) is showing continuity to a known ground (ie the frame). If it does show little to no ohms of resistance then this eliminates the possibility of a bad ground.