Come Early, be bold.
I arrived at the campsite at 11 am on a Friday. All the sites were filled and I had not been to this site before. I lost hope fast but I drove around a few times and my co-adventurer had the bright idea to actually ask people if they are leaving. (This was clutch). If you plan on finding a first come first serve sight at J tree. Make sure you are willing to approach campers or have someone that will. Because if you don't you will not find a sigh unless it is already vacant which is rare.
One thing that I noticed about this campground is how intimate it is. On many of the blocks of sites, there are no natural barriers between sites. So if privacy is what you are seeking this may not be the best choice. This can also cause some tension between campers that feel you have set up on "their site" even when there are no clear barriers.
More on the intimacy. If you don't know J tree is coveted by rock climbers and people that boulder. Site 29 and 30 are right on the path to get to routes or have a bouldering section right on them. It was a little funny to have people walking right through my camp but I quickly realized it was normal for the reasons above. Something to think about.
Quiet hours are QUIET. I have a feeling this was the case because most of the other campers were climbing most of the day and probably knocked out early to get good rest. Whatever the reason it was strange having the camp completely silent before and continuing after 10 pm even on a Weekend!
If you get a site here you are going to love it. The setting is jaw-dropping and makes every moment dreamy. Except when you have to pack up and leave. Hope this helps!