I have been tinkering with GeoGebra to construct a point on a circle that I can move around the circumference which then in turn moves another point on another circle at a slower rotation rate (specifically 3:2)? All I can do is to make it match the same rotation rate.
You can see the set up for that in the image below. All it is showing is as I move point "E" around the circle at the origin point "H" travels the same path in a different spot.
It is impossible to do that with a purely geometric construction. After a full revolution point $E$ comes back to where it started from, so its final position is indistinguishable from the initial position, but point $H$ will not return to its initial position. In other words: the map $E\mapsto H$ is not a geometrical function, you need some mechanism to count how many revolutions have been made "since the beginning".
It is possible however that some trick may do the job, either with GeoGebra or some other software.