Well, 18 USC 930 doesn't cover it either. It refers to "Possession of firearms and dangerous weapons in Federal facilities" and defines a federal facility as:
The term “Federal facility” means a building or part thereof owned or leased by the Federal Government, where Federal employees are regularly present for the purpose of performing their official duties.
This seems to clearly limit itself to structures and only some structures at that. Unless the unauthorized firearm is carried into a building on the base, this statute wouldn't apply. If the firearm is in a vehicle in a parking lot or the person carrying the firearm doesn't go inside a building, it doesn't appear that this would be a valid statute with which to charge a person.
As for the VA hospital, there's a section in the CFR's that deal with weapons on VA property
38 C.F.R. § 1.218
Weapons and explosives. No person while on property shall carry firearms, other dangerous or deadly weapons, or explosives, either openly or concealed, except for official purposes.
39 CFR 232.1 has a similar prohibition for firearms on Post Office property, such as a parking lot) although 18 USC 930 covers the building(s):
39 CFR 232.1 (k)(1)
Weapons and explosives. Notwithstanding the provisions of any
other law, rule or regulation, no person while on postal property may
carry firearms, other dangerous or deadly weapons, or explosives, either
openly or concealed, or store the same on postal property, except for
I cannot find anything similar that covers unauthorized firearms on military property
exclusive of buildings.