Trunk was born in Tauberbischofsheim on 10 February 1879. In 1894 he began his studies at the Hoch'sche Konservatorium with Iwan Knorr in Frankfurt. From 1896 to 1899 he studied at the Royal Academy of Music in Munich with Joseph Rheinberger and Berthold Kellermann. He then worked in Munich as a music teacher, accompanist and conductor of two singing societies, the Bürgersängerzunft and the Volkchor Union, as well as piano accompanist to Eugen Gura, and from 1906 to 1909 as music editor of the "Münchner Post" and as a composer. In 1912 he went to New York as director of the Arion Society, where he remained until the outbreak of the First World War. Afterwards he worked again in Munich as a composer and music writer (1916-1922 as a contributor to the Bayerische Staatszeitung) and from 1919 again as a conductor of the Bürgersängerzunft and as an accompanist in Munich.
From 1925 he worked at the Rhenish Music School in Cologne, first as deputy director, and from 1933 as director, having become a professor there in 1927. In 1931 he joined the NSDAP (membership number 659.692). In 1934 Trunk became president of the State Academy of Music in Munich. From 1935 to 1939 he was conductor of the Munich Teachers' Singing Society.
From 1909 he was married to the singer Fanny Echter. After their divorce, he married the singer Maria Delbran in his second marriage in 1925. After 1945 he lived in seclusion in Riederau am Ammersee until his death in 1968.
