Eelsingh was born on 1 September 1903 in Zwolle. She studied with . Eelsingh was a member of De Brug, De Ploeg, and the . She was the recipient of the Koninklijke subsidie voor vrije schilderkunst (Royal grant for free painting). Her work was included in the 1939 exhibition and sale Onze Kunst van Heden (Our Art of Today) at the Rijksmuseum in Amsterdam.
