If you're enjoying Yukon's campgrounds, you'll see mostly Canadians and Europeans. Americans seem to prefer the commercial campgrounds or the Whitehorse Walmart.
When we travel off the main roads, we'll see B.C. plates, some Alberta & Ontario plates, and rentals with European tourists. But few U.S. plates.
Pine Lake might be a bit busier tomorrow, as it will be Saturday night. Locals like that spot for the fishing. Perhaps consider Million Dollar Falls Yukon gov't campground on the Haines Road. It's a nice location and there are some nice hiking trails around there. Plenty of sites that will take your rig. It's a quiet location too, even on a long weekend it tends to be quiet.