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On the park website, it says that parking facilities are still open:
Facilities, services, and features that are open:
[...]
Roads and parking lots. Please park only in designated parking spaces. If a parking lot is full, refer to the park newspaper for other options.
The parks veichles length restrictions page states that vehicles longer than 24 feet are not advised.
You can not park next to the tree anyway unless you have a disability parking placard:
Those with disability parking placards can park in a small lot along the edge of the Generals Highway. From there, a wheelchair-accessible trail leads a short distance to the tree. If you don't have a placard but can't manage the Main Trail, during shuttle season you can ride park shuttles (all are wheelchair accessible, and some kneel) to the accessible trail.
(source)