I know you can buy tickets, not sure which ones
I'm think you can buy it there. The south entrance didn't have a mail drop, but mail can be dropped off here. It's also a fancier Visitor's Center. The art work is remarkable!
You can buy the main pass for the park at the visitors center. If you need a disabled pass or military pass you will need to drive up to the gate on Utah or the joshua tree or cottonwood entrances. The gates can process credit card payments. Lifetime passes (free) for permanent disabled are available at the gate entrances
Can purchase at the visitor center or at any pay station.
I think you can buy one there. If not in the other entrance. The Joshua Tree Visitor center
Thanks! Your answer is awaiting moderation.