In 1778 Runk graduated from the Academy of Fine Arts Vienna, and studied with among others Hubert Maurer, Friedrich August and Johann Christian Brand.
Soon after completion of the Academy, he was very successful, in addition to oil paintings mainly with gouache, his preferred technique.
He lived and worked mainly in Bohemia, mainly in Český Krumlov, but also in Styria, in the service of Joseph II of Schwarzenberg (1769–1833).
Between 1803 and 1810, an intense friendship and collaboration with his pupil and patron Pauline Schwarzenberg, the wife of Joseph II.
Many of his works can be found in the Graphic Collection of the Academy of Fine Arts and in the Albertina museum in Vienna today.