John: Add #3 if you are in Idaho. A LEO can enter private property (eg: An RV campground) if they have an articulable suspicion that a crime is in progress, there. ("Articulable suspicion" is "Probable Cause.")
In my volunteer work, I have provided that "articulable suspicion" at a campground, here, between two city parks. The manager was very grateful! (We have stayed there, many times, in our motorhome.)
They can also continue an active pursuit through private property. Done that, too. (Except that as a volunteer, even if I am in uniform, I am not authorized to "pursue." I am authorized to "follow." ??? :
;D )
Shortly after we got our first motorhome, about four years ago, I ask a cop I work with about open alcohol containers in a motorhome. He said if the container was in a front seat, or could be reached from there, and the vehicle was on a public road, moving or not, he would cite. He wasn't sure, but thought it was legal, in the fridge. In any case, he said he wouldn't look in the fridge, unless he suspected there was other contraband in there, and then he would ignore any open container of alcohol. Also, he noted that he doesn't do traffic patrol, and would have to refresh his memory, if he were asked to do that type of work and had to deal with a motorhome.
Ray D