RT66 between Kingman and Ashfork is the old road and maintained in reasonable condition for travelers as we have traveled it numerous times. Stop at Grand Canyon Caverns, located just a few miles east of Peach Springs, Arizona, They are among the largest of dry caverns in the United States and they have a campground onsite. There is quite a bit of open and private land along this route but I would check before venturing off the beaten path. There are many roads off RT66 that have signs posted to gates with information if entering the areas.
I noticed you did not asked about RT66 between Kingman and Oatman but for your information I would not recommend you take the trailer on RT66 from Kingman to Oatman as it is very narrow, quite a grade and many switchback, I believe there is signage stating not recommended for TT or vehicles over a certain length.
Have a great trip.
