After Ferrari refused to enter the 1962 Mexican "Grand Prix", the first to be held in Mexico, Rodríguez and his younger brother both found rides of their own. After his brother was killed in a horrific accident in practice, Rodríguez withdrew. He considered retiring from racing. However, in 1963 he won the Daytona Continental in a 250GTO entered by North American Racing Team. He came third at Sebring, sharing a 330TR/LM with Graham Hill. He failed to qualify at Indianapolis, in an Aston Martin-powered Cooper T54, but took part in his first "Grands Prix" in the works Lotus at Watkins Glen and Magdalena Mixhuca. Rodríguez failed to finish both times.