The wearing of rings – and thus gemstones – on specific fingers and phalanges is encouraged by a Vedic Jyotish (astrologer) as a propitiatory gesture during certain planetary transits. The planet Saturn according to the Vedic tradition is sacred to the blue sapphire, the Neelam stone in sanskrit, indeed all the planets and even the two lunar nodes, have their individual gemstones making nine in total – the navrattan of gemstones in the Vedic tradition.
This is not the place to expand on this further but it may perhaps be the reason why the Saturn finger has been avoided even in Europe where the ancient Vedic astrological tradition is little known, except as a basis for superstition. When the origin of a wisdom is forgotten it tends to survive as superstition and folklore.
It may also perhaps help to explain why none of the wives of Henry VIII were depicted wearing a ring on the Saturn finger.