I work for the one in my State and I am not speaking on their or any others behalf or am I at any level within having any power or authority to make agreements or to give any permission or approve permitting. I do though think I'm safe to say as long as you are not on an Interstate Right of Way, as long as your vehicle has current tags and insurance, as long as it is safely parked out past the Fog Line or not in a no parking area and not obstructing sight, signs and such, as long as you are not crossing the highway becoming a hazard to yourself and the traveling public, not leaving things or hazards in the travel lanes, not using wheel or track and fuel powered machinery to dig or alter the Right of Way, and are not rolling rocks down in to the borrow ditch or moving materials that would fill it or aggravate erosion, not wrecking fences, digging up survey or monument markers,
I doubt very much we would bother to stop for someone detecting a dirt turn out for instance. So far I have not or have the guys I work with that I know of but could if we thought something was not right, causing damage, or was unsafe. Here on my section, especially since winter is getting closer and the maintenance is coming to an almost stand still, we are patrolling more often now to check the road condition and as always, looking for hazards and signs down for instance. Now the Rest Stops may be an issue as some have Contract Tenants that live on site as does ours. Our contract grounds keeper who cares for our Rest Stop metal detects and has detected this one. Knowing them a bit, I doubt they would say much as long as others were not killing the lawn and stuff like that or digging up the sprinkler heads.
The situation you are speaking of though may not be one you will want to chance. If any of our State property or areas of Right of Way has for instance "No Trespassing" signs, black letter on white background or white letter on black background, it is the Law. We have on our section, two locations that are signed. One is a waste materials dump area and our Yard and Shed is not only fenced and gated but is signed with such besides having another sign at the entrance with "Emergency Vehicles Authorised Personnel Only" and means exactly that. Now we don't get butt ugly about it when people drive in for need of help, or to report to us something but we have also had people just drive in having no reason at all to be here and we will challenge and ask them to leave. If they refuse, we just call Law Enforcement and so far, that has not happened. We are not Law Enforcement but we are around them often.
Like I said, I'm no authority to say one way or another, just passing on what my experience has been. If it were me, private citizen, and the signs no mater color, hand made or official and said "No Trespassing," I'd take it as such and move on. Here in Idaho, all a land owner has to do is paint a corner fence post for instance and then so much distance in between them with I think it's fluorescent red or orange, 4" X 4" area or greater, it means no trespassing. I've even seen rocks painted where there is no fence and it is legitimate.