Eichmann began his career in 1978 in German Formula 3 , where he competed from 1978 to 1980, 1982 (runner-up) to 1983 and 1986 (26th overall). He also drove in European Formula 3 from 1978 to 1980 . In 1980 (18th place overall) and 1981 (3rd place) he competed in the VW Castrol Europe Cup. In 1980 and 1982 he also competed in the Formula 2 European Championship. In 1987 he left formula racing and drove in the Renault Alpine v6 Europe and finished 16th at the end of the season. In 1988 he switched to the Renault Elf Turbo Europe Cup and was 15th overall. In 1989 he switched to the German Touring Car Championshipin which he contested isolated races in a private BMW M3 from the Tauber Motorsport team. In 1990 (11th place), 1991 (10th place) and 1992 (runner-up) he competed in the German Porsche Carrera Cup. In 1993 he switched to the Porsche Supercup and came fourth in the overall standings. At the same time he contested the season in the ADAC GT Cup and finished sixth in class 1. In 1994 he drove in the Swiss Touring Car Championship and in the German Super Touring Car Cup, in which he was 17th overall. In 1995 he switched back to the German Porsche Carrera Cup and was 10th overall. He also drove in the ADAC GT Cup again and was third in class 1. In 1996 he drove the Le Mans 24 Hours and won the GT2 class. He also drove in the 1996 Global GT Championship and came third in the overall standings. In 1997 he drove again in the 24 Hours of Le Mans and this time came second in the GT2 class. He also drove in the newly founded FIA GT Championship in 1997 and came second in the GT2 class. In 1998 he stayed loyal to the series and finished fourth in the GT2 class. In 2001 he drove again in the FIA GT series and finished 22nd in the NGT class.