First off, I would suggest you speak with a lawyer.
Second, I don't think you CAN be landlocked. Again, talk to a lawyer, but I believe you have an easement by right of use. I know with my property, I must chain and or deny access, at least one day per year, or my road can become public access.
Third THANK YOU FOR YOUR SERVICE, SIR! You have rights to hunt your own property as long as it is in a hunt-able area, such as outside city limits, not because of your service, but because of your ownership. In my neck of the woods, owners require no permits either.
Now your service DOES have hunting advantages. Check your local laws, but here, active servicemen on leave get a free pass, Check with your local DNR as well, to find out all your hunting, fishing, and trapping benefits, because of your service.
Lastly,as to the neighbor....I would thank him for the generous offer to let you hunt HIS LAND, because "He said it's not the neighborly thing to hunt on my land" and since your land is unsuitable in his eyes, he must be offering you HIS to be "neighborly."
The only real difference between a good tracker and a bad tracker is observation. All the same data is present for both. The rest is understanding what you are seeing.