https://www.huntington.org/plan-your-visit This page has the information you need. April 6 is the next time you can reserve tickets for the following 2 weeks.
It's open you don't need a reservation
I believe it's open for booking every couple of weeks but it's selling face due to spring time bloom and people are starting to come out
The next ticket release date is Tuesday, April 6, at noon.
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