Two nulls, Null 1 to control the center of rotation and overall placement of brush, Null 2 for the rotating motion.
Null 2 position expression
thisComp.layer("Null 1").transform.position+[200*Math.cos(time*5), 100*Math.sin(time*5)]
Parent the brush to null 2. Adjust values for your needs.
You can add a wiggle to the position of Null 1 to give it some variation.
Kalleheikki Kannisto
Senior Graphic Designer