Although Brabham reverted to the team's interim Lotus to win the non-Championship Danish Grand Prix three weeks later, by the time of the Oulton Park International Gold Cup a few days following he was once again driving the new car. After starting fifth on the grid, Brabham rose to third by the final flag – despite having to nurse rapidly wearing brake pads – to take his first podium position in a car bearing his own name. He then sat out the high-speed Italian Grand Prix at Monza later that month, owing to a disagreement with the race promoter regarding starting money, before returning the BT3 to Championship duty to take fourth places at the final two rounds of the season, the 1962 United States and South African Grands Prix, scoring the new marque's first Constructors' Championship points, and the first ever Championship points for a driver in a car carrying his own name. Between these two events Brabham took second position in the inaugural Mexican Grand Prix, the only man to finish on the same lap as eventual joint winners Jim Clark and Trevor Taylor in their Lotus 25.