Gullikson and his twin brother Tom attended Northern Illinois University. After his studies he worked as a tennis coach. Initially he played on satellite tournaments, in 1977 his breakthrough came with three individual titles, which he was awarded by the ATP Newcomer of the Year as out. In addition, he stood with his brother Tom twice in a double finals, but they lost each. In 1978, he won his fourth and last single title in Johannesburg, as well as to his brother's side three doubles titles. Of the total of 15 double titles of his career, he won ten along with his brother. Its highest listing in the tennis world ranking he reached in 1979 with position 15 in the singles and 1983 for third position in the doubles.
His best individual result at a Grand Slam tournament was the quarter- finals at Wimbledon in 1979. In the doubles competition, he reached in 1983 with his brother the finals of Wimbledon, but they lost Peter Fleming and John McEnroe in straight sets. Furthermore, he was in the semifinals of the Australian Open and the U.S. Open.
After the end of his professional career, he was a tennis coach. , He worked on Martina Navratilova, Mary Joe Fernandez and Aaron Krickstein. Later he was responsible for the then world number one Pete Sampras. At the Australian Open 1995 suffered Gullikson, which later was diagnosed with a brain tumor, a dizzy spell. Sampras broke then later in his match against Jim Courier in tears. Gullikson died in May 1996.