During his youth he played association football for SK Brann, eventually becoming team captain before World War II.
During the war Eilertsen studied medicine in Oslo, but never finished his education, as he joined the resistance movement and had to flee to the United Kingdom.
After the war ended in 1945, he finished his studies at Harvard University in the United States, before returning to Norway to practice.
After stepping down as mayor in 1984, Eilertsen became involved in medicine once again, working with the organization and financing of Norwegian hospitals and trauma centres.
Eilertsen remained in Bergen after his retirement, where he died on 24 February 2014, the day before his 96th birthday, of natural causes.