At the University of Texas, Gooch was a member of the
Southwest Conference championship track teams from 1925 to 1927 and won the 1927 conference discus championship. He also won the Southwest Conference's 1926 heavyweight wrestling championship. At a Southwest Conference track meet, Gooch, who had a reputation for heckling his opponents, was warned by event official
John W. Heisman (also the Rice football coach at the time) that he would be disqualified if he said one word to his chief opponent. Gooch reportedly sat down where he could be seen by his rival and held his lips together with his fingers. After his opponent fouled, Heisman chastised Gooch for violating orders, and Gooch replied, "I did exactly what you said. I not only sat down and didn't say anything but I held my mouth shut so I couldn't." Gooch was also selected as an All-Southwest Conference tackle while playing for the Longhorns football team. In September 1926, the
Associated Press reported that Gooch had reported for football practice "in splendid condition after wrestling all summer with blocks of ice." In November 1926, the Galveston Daily News wrote: "Gooch is another player who has improved rapidly this year. He formerly had difficulty in shifting his big feet, but apparently has overcome this disadvantage. Gooch is one of the hardest fighting tackles the Longhorns have had since the days of Eddie Bluestein. Moore and Gooch make a splendid combination." While attending Texas, Gooch was also the president of the "T" Association and a member of the
Theta Xi fraternity. ==Legal and political career==