Todd, I had the same problem, PTO would not engage. Since I have 3 JD318s I swapped PTOs and it still would not engage. Then I swapped them back and neither would engage! So I bought a new PTO for one tractor and that worked fine. For the other tractor I just bought the big round metal part that goes inside the PTO (forgot what it is called). That would not engaged until I adjusted the gap. What I learned from all this is to check the PTO gap first! Try to tighten it and see if that helps. Also check the resistance in the PTO. It should be 4.5ish, if it is reading close to 0 like mine was you might need that big round metal part inside the PTO. $170.00ish at JD where a new PTO will cost you $350.00ish at JD. I'm pretty sure the only part that can short out inside the PTO is the big round steel part.
To sum up
Listen very carefully when you engage the PTO you should hear a slight click. If so the wires are correct. Next check resistance 4.5ish is prefect, lastly carefully tighten gap just a little bit at a time until PTO engages. Hope this helps.