Tauson played mainly on the ATP Challenger Tour. In 1988 he won at the side of Morten Christensen the doubles title at the Challenger tournament in Hanko, a year later, he became the qualifier the Challenger Tournaments of Croydon and Telford and reached the final of Heilbronn, where he lost the final Michael Stich. In 1990, he reached the semifinals of the ATP tournament in Rotterdam, where he Michiel Schaper, Paul Haarhuis and Magnus Gustafsson Brad Gilbert finally succumbed to Siegen. His best result on the double ATP World Tour was a semi-finals in doubles at the Swedish Open. Its highest listing in the tennis world ranking he reached in 1990 with position 101 in the singles and 118th in doubles in 1987.
His best individual result at a Grand Slam tournament was the second-round participation at the French Open in 1989, two years earlier, he had also reached the second round at the French Open in doubles.
Tauson completed 1985-1991 25 single and five double appearances for the Danish Davis Cup team. There he succeeded in doing individual victories against Horst Skoff, Thomas Muster and Emilio Sánchez Vicario. His greatest success with the team was participating in the quarterfinals of the World Group, which went 0-5 lost to Germany, where he made two individual against Eric Jelen and Boris Becker and also the double on the side of Michael Mortensen. He joined the Summer Olympic Games in Seoul in 1988 on both single and double for Denmark. On the side of Morten Christensen he reached the quarter-finals, they lost there but the later gold medal winners Ken Flach and Robert Seguso from the United States. In the individual he was defeated in the first round against Brad Gilbert.