I didn’t completely understand how permits worked for some of these trips when we went to Silver Lake. I have a National Parks year pass, which also gets me into national forest and public lands, so I was able to get into the Unitas and Wasatch National Forests for free. When we got to the trail head at Silver Lake, we eventually found a box with envelopes for our parking pass, which we paid. I think I might’ve been able to just stick my National Parks pass in the window and we would’ve been good.
Basically if you have a National Parks pass, you just have to put that in your car’s windshield and it will be your permit for your car. I would always check with the local park ranger for back country permits because with lesser known hikes you won’t need a permit. With Silver and Island Lake, we didn’t need any permits, but other trips you might especially with trips in National Parks.