Rest area overnight Montana and Idaho

I don't know of any. I would check out Free Campgrounds which often list overnight areas. We've traveled form Boise to Glacier and stayed over in grocery parking lots, like the one time we stayed in Salmon. DH went in and checked with the manager and they said no problem. We bought breakfast there the next day. Also stayed in the parking lot of a grocery store in McCall, Idaho and did the same thing.