[With regard to any county which is required to operate on a countywide system of road administration as described in Section 19-2-3, this section shall read as follows:]
Whenever in the discretion of the board of supervisors of any county it seems proper so to do, the board may, by order on its minutes, authorize the road manager of the county or the county engineer to forbid the use of any hard surfaced road, or portion thereof, when under construction or repair. The county road manager or the engineer, when so authorized by the board of supervisors, may close said road or any portion thereof to travel by an obstruction placed thereon in such manner as to indicate its closing, or by a sign marked “closed by order of the county road manager (or county engineer).”