There are several spots out there. I’ve shown up at midnight on a Saturday in August and still found a spot. Just be aware that the road can get really rough the deeper you go back in. I pulled a 30’ trailer to the very end of the line and made it ok. Just watch out for areas where the road is washed out.

You'll find something but it probably won't be the best spot -- it will be along the main road or just off one of the side roads instead of the best spots further up against the rock formations. I'd also try to show up with some light left, there's a number of separate roads that lead into South Temple Wash that could be hard to navigate in the dark.