Information concerning soldiers being thrown from horses or spilling hot coffee won't be found in service files. You could review the service files of soldiers named Vance who served in North Carolina units to see if any of them died due to accident.

If you knew the name a witness and found his service file, you could assume that "Vance" served in the same command. That would make your search easier, since Vance could be a first or last name, or just a nickname.

Any other particulars would be helpful. Unless there's a lot more to it, this acount is likely to remain in storyland.