Tucson Camp Ground, Gilbert Ray?

We will be in the Tucson area next week, and the Gilbert Ray camp ground sounds like a great place. It's a "first come first served" camp ground so I'm wondering if any of you have experience with site availability.

If we were to arrive on a Monday or Tuesday morning what would be the chances finding a spot?

Tucson has been on our bucket list for about four years now, and we're both stoked to finally get to spend some time there to explore.

Thanks in advance.