The shadow of the rings on the planet is a somewhat more difficult feature.
The shadow of the planet on the rings is best seen when the rings are well open and the planet is in or near quadrature.

It is to be looked for to the left of the ball (in an inverting telescope) at quadrature preceding opposition, and to the right at quadrature following opposition.

Saturn is more likely to be studied at the latter than at the former quadrature, as in quadrature preceding opposition he is a morning star.

The shadow of the rings on the planet is best seen when the rings are but moderately open, and Saturn is in or near quadrature.
When the shadow lies outside the rings it is best seen, as the dark ring takes off from the sharpness of the contrast when the shadow lies within the ring.

It would take more space than I can spare here to show how it is to be determined (independently) whether the shadow lies within or without the ring.