The stage direction "eccentric business" sometimes appears in playscripts of the era, often when a featured actor in comedy is alone on stage. The performer would be expected to draw upon his or her personal tricks of the trade for comic effect. These amusing idiosyncratic activities might involve some anomalous handling of props or simply grotesque movement and gesture. "Eccentric comedian" was another term for a character actor specializing in quirky comedy.
The Historical Dictionary of the American Theater. James Fisher.