Eunice debuted in 1990, running four late-season races. Starting 14th at Volusia, Eunice had an engine expire and would finish 26th. Despite the trouble, it would be Eunice's best race of the year, despite the fact that he did finish a race at Charlotte, the only one he would finish on the year.
Eunice stepped his schedule up to twenty races for 1991, but only recieved minor success. He only earned one top-ten: a 10th at Dublin. However, he would earn 12 top-twenties in those twenty starts, showing the ability to have consistenly decent runs. In addition, as a rookie, Eunice was able to finish 80% of his starts, which is an impressive number. Only two of those were crash related. He would end up 24th in the points, his career best.
Eunice's last start came in 1992, after his Levin Racing team had shut down. Driving a car that was not numbered "19" for the first time in his career, Eunice drove the #02 Oldsmobile to a soild 18th place finish at Charlotte. However, the ride did not materialize for more races and Eunice has not raced since.