Hidden valley on a Monday?

Heading up to Joshua tree in a week or so arriving Sunday evening and getting a hotel Sunday evening but hoping to score a campsite at hidden Valley on Monday, any beta on getting a first come first serve site?

what are our chances if we are there late morning on Monday of getting a site?

That is a good time to look! Usually Sunday will be the best time when weekenders leave. However, this Monday is Veterans Day so perhaps parties with the day off will leave on Monday.

I have also ditched my car in town and gone ultralight in the park, much easier to share a site that way.