That's what signs are for, I lived deep in the woods for 3 years, had a 1/2 mile lane and a large creek that flowed threw the property, people would drive back thinking it was a road ext.
I did work for a sign company, they made all the street signs for Columbus Ohio, I asked them if they could make me a couple signs, one was a bridge weight limit sign and the other a red and white do not enter sign. I put the do not enter sign along with a posted private property sign out by the entrance and that stopped the random strangers from driving back, tourists is all they were, out for a drive in the country, for whatever reason the open gate wasn't a sign of private property lol.
But lost hikers would still show up and also tubers and kayakers in the creek. No way to keep everyone out.
If they think you have something valuable, it's worse. But it's guys like this that help scare the crap out of hearing a gun shot if there doing something wrong.
Would I ever shoot someone outside of my house that's not a danger to myself or my family? No, I will stop them and point them in the right direction though, hikers get lost all the dang time, saves them miles of hiking back to the car on the road if they are pointed the right direction in the woods.
Usually I give people the benefit of the doubt, if there breaking in, I'll chase them off, but to be honest I have never had to yet.