The first place to check is Handgunlaw.us. On page 7 of the SC information, I found:
Section 16-23-20. Unlawful Carrying of Handgun; Exceptions.
(9) a person in a vehicle if the handgun is secured in a closed glove compartment, closed console, closed
trunk, or in a closed container secured by an integral fastener and transported in the luggage compartment of
the vehicle; however, this item is not violated if the glove compartment, console, or trunk is opened in the
presence of a law enforcement officer for the sole purpose of retrieving a driver’s license, registration, or
proof of insurance; If the person has been issued a concealed weapons permit pursuant to Article 4, Chapter
31, Title 23, then the person also may secure his weapon under a seat in a vehicle, or in any open or closed
storage compartment within the vehicle’s passenger compartment; or”
My advice, to be safe, is for you to contact the SC State Police and ask them if the above is correct for someone traveling through the state.