Technically? The spell, Flesh to Stone, won't work on an incorporeal creature (likewise, anything that inherits from Flesh to Stone won't), as the descriptions includes "Only creatures made of flesh are affected by this spell." Other effects (such as Prismatic Spray) technically will turn a living incorporeal creature (such as, say, an Unbodied) into stone. That's somewhat silly, mind, but exactly as written, it's correct.So incorporeal non-undead will be affected by petrifying effects normally?
2nd Edition Advanced Dungeons & Dragons said:These reptilian monsters all posses a gaze that enables them to turn any fleshy creature to stone; their gaze extends into the Astral and Ethereal planes.
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Combat: While it has strong, toothy jaws, the basilisk's major weapon is its gaze. However, if its gaze is reflected, and it sees its own eyes, it will become petrified itself, but this requires light at least equal to bright torchlight and a good, smooth reflector. In the Astral plane its gaze kills; in the Ethereal plane it turns victims into ethereal stone. These will only be seen by those in the Ethereal plane or who can see ethereal objects.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.