How about a sign that simply reads
DANGER
Live fire range
Authorized personnel only
We too have a well posted private road with a gate. If the gate is closed it keeps out vehicles but we still get people who walk in from time to time. Last year after a heavy snow storm two neighbor twits walked in and put foot prints all over the road. I noticed when I went out to take a photo of the road with snow. NOT the image I was looking to capture. Years back a similar thing happened except I drove 50 miles round trip to get the photo but the neighbor hood twit used an ATV.
Signs only do so much.
I know a POlice range that is well marked as such. No trespassing, authorized personal only, firing range, live firing, trespassers will be prosecuted, etc signs all over the place.
Two dumb butts walked into the property after parking their truck near the range gate. No way they could miss the signs. They were hunting. By the time it was over with they were arrested by Wildlife Officers and they were danged lucky to not get shot.
If you are STUPID enough to trespass on such a well marked property as a police range no sign will work.
Another time two adults used the entrance of the police range to have a clandestine meeting of the adult kind. I guess hormones stopped their ability to read and think since they were surprised when a bunch of officers left the range and the two adults were caught in the act.
You can really only do so much with signs, gates, and fences.

People are going to snoop. People are going to trespass. And Stupid is as Stupid does. You just cannot stop Stupid. You can just minimize what Stupid does.
We do keep our gate looking like a farm road gate. One cannot see our house from the gate. We keep the gate looking simple and unassuming though we would like to make it look nicer and put up some planters and such. Instead we just keep it looking like a simple gate on a farm road.
Later,
Dan