If a driver is going to arrive at the border after business hours he will fax his customs paperwork to the customs broker who will clear the shipment and leave the paperwork in a box at the border. When the driver arrives at the border he picks up his paperwork and takes it to customs. Thus, the driver can clear at the border 24 hours a day.
Generally inland brokers (those not located at a border) will not clear shipments after regular business hours. In many cases these brokers will have an agent at the border who can clear shipments on their behalf, but the agents will require prior authorization from the broker in order to clear.