I found the SC provision before Mark Adams did and shared it with others, but kudos for getting on the radio and talking about it to Mark Adams. If there were an action in SC I'd support it, here's the specific clause in question reprinted here:
http://www.democraticunderground.com/discuss/duboard.php?az=show_mesg&forum=177&topic_id=1382&mesg_id=1383 SECTION 1. Elections to be by secret ballot; protection of right of suffrage.
All elections by the people shall be by secret ballot, but the ballots shall not be counted in secret. The right of suffrage, as regulated in this Constitution, shall be protected by laws regulating elections and prohibiting, under adequate penalties, all undue influence from power, bribery, tumult, or improper conduct.
SECTION 2. Free exercise of right of suffrage.
No power, civil or military, shall at any time interfere to prevent the free exercise of the right of suffrage in this State.
In Virginia it's the article I, sec. 15. Here again, none of us are the first to ever read these state constitutions, but on the other hand some of the more obvious violations tend to show that no one is paying attention to them frequently enough. In the VA constitution it says
Virginia Const. Art. II, sec. 3, para. 2 Secrecy in casting votes shall be maintained, except as provision may be made for assistance to handicapped voters, but the ballot box or voting machine shall be kept in public view and shall not be opened, nor the ballots canvassed nor the votes counted, in secret. Votes may be cast in person or by absentee ballot as provided by law.
Comparing the two, the SC is a little stronger, since in an unquoted provision VA's constitution does mention voting machines, yet the no secrecy provision should require at least discovery on an expedited basis of the workings of the hard drives that did the counting so experts could try to interpret that, which is much more than we have now. (though to anyone not fluent in computers it is the same as having info provided in greek)