Born in San Sebastián, Elduayen made his professional debuts with local Real Sociedad, being barred by legendary Luis Arconada.
In the 1985–86 season, however, as the starter suffered a severe injury in the first La Liga game, he was chosen by manager John Toshack as his successor, and the Basques eventually finished in seventh position but with one of the worst defensive records in the competition (51 goals against with 34 matches from the player).
In the 1986 summer, Elduayen signed with fellow top flight club Atlético Madrid, starting in his first year but being relegated to the substitutes bench after the emergence of Abel Resino, who had been playing with the reserves.
He experienced his best years with Real Burgos CF, helping the lowly Castile and León side to three consecutive seasons in the first division.
In 1991–92, as they finished in a best-ever ninth position, he played in all 38 games (3,338 minutes) and only conceded 43 goals, winning the Don Balón Award for Best Spanish Player in the process.