You can stay after the closing time with a fishing permit or by camping there. The closing time is posted at the park after you pass the entrance. The latest it's open is 8:30 around the summer solstice. Now in August it's back to 8:00 already.
Unfortunately, no it is not open to stargaze BUT it you ever decide to camp at HBSP there’s very little light pollution so you get to see a ton of stars right from your campground. Hope this helped !
They usually close at sundown. But you can access the beach from the camping area.
Have to leave at sunset.
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